{"id":6677,"date":"2026-07-19T09:12:13","date_gmt":"2026-07-19T09:12:13","guid":{"rendered":"https:\/\/oratrics.com\/blogs\/?p=6677"},"modified":"2026-07-19T10:36:28","modified_gmt":"2026-07-19T10:36:28","slug":"prime-factorization-of-10500","status":"publish","type":"post","link":"https:\/\/oratrics.com\/blogs\/math-explorer-program\/prime-factorization-of-10500\/","title":{"rendered":"Prime Factorization of 10500 : Step-by-Step Method with Solved Examples"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"6677\" class=\"elementor elementor-6677\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7ce6370 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"7ce6370\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-36f17c2\" data-id=\"36f17c2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4236e07\" data-id=\"4236e07\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f406a7e elementor-widget elementor-widget-heading\" data-id=\"f406a7e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Prime Factorization of 10500 : Step-by-Step Method with Solved Examples<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7c5b1c1 elementor-widget elementor-widget-text-editor\" data-id=\"7c5b1c1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">The prime factorization of 10500 is 2\u00b2 \u00d7 3 \u00d7 5\u00b3 \u00d7 7. If you just needed the answer for homework, there it is. But if you got that answer from a calculator and now have to show your working (which, let&#8217;s be honest, is what actually happens in most Class 6-8 classrooms), you&#8217;ll want to know how those four numbers were found in the first place. That&#8217;s what this article walks through not just the what, but the &#8220;how&#8221; and, more importantly, the why it always works out this way.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-770bc1a elementor-widget elementor-widget-image\" data-id=\"770bc1a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/07\/ChatGPT-Image-Jul-19-2026-03_54_40-PM-1024x683.webp\" class=\"attachment-large size-large wp-image-6765\" alt=\"What is the prime factorization of 10500\" srcset=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/07\/ChatGPT-Image-Jul-19-2026-03_54_40-PM-1024x683.webp 1024w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/07\/ChatGPT-Image-Jul-19-2026-03_54_40-PM-300x200.webp 300w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/07\/ChatGPT-Image-Jul-19-2026-03_54_40-PM-768x512.webp 768w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/07\/ChatGPT-Image-Jul-19-2026-03_54_40-PM.webp 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-cdd3f0c\" data-id=\"cdd3f0c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bd88573 elementor-widget elementor-widget-html\" data-id=\"bd88573\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t\t<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\r\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Poppins:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\r\n\r\n<div class=\"toc-wrapper\">\r\n    \r\n    \r\n    <div class=\"custom-toc\" id=\"custom-toc\">\r\n        <div class=\"toc-title\">\r\n            \u2630 Table of Contents\r\n        <\/div>\r\n        <ul class=\"toc-list\" id=\"toc-list\"><\/ul>\r\n    <\/div>\r\n    \r\n<\/div>\r\n\r\n<style>\r\n\/* Parent Fixed Wrapper holding both components together *\/\r\n.toc-wrapper {\r\n    position: fixed;\r\n    top: 150px; \r\n    z-index: 1 !important;\r\n    right: 70px;\r\n    width: 100%;\r\n    max-width: 340px;\r\n    font-family: 'Poppins', sans-serif;\r\n}\r\n\r\n\/* Image Styling *\/\r\n.toc-sticky-image {\r\n    width: 100%;\r\n    height: auto;\r\n    border-radius: 22px; \r\n    margin-bottom: 15px; \r\n    box-shadow: 0 4px 12px rgba(0,0,0,0.05);\r\n    display: block;\r\n}\r\n\r\n\/* TOC Container *\/\r\n.custom-toc {\r\n    background: #fff;\r\n    border: 1px solid #dfe3ea;\r\n    border-radius: 22px;\r\n    padding: 0px 28px;\r\n    width: 100%;\r\n    max-height: 24rem; \r\n    overflow-y: auto;\r\n    box-shadow: 0 2px 8px rgba(0,0,0,0.03);\r\n}\r\n\r\n\/* Title *\/\r\n.custom-toc .toc-title {\r\n    font-size: 25px;\r\n    font-weight: 700;\r\n    color: #17233c;\r\n    position: sticky;\r\n    padding: 0.6rem 0rem;\r\n    background-color: white;\r\n    top: 0px;\r\n    margin-bottom: 12px;\r\n    display: flex;\r\n    align-items: center;\r\n    gap: 10px;\r\n    z-index: 2;\r\n}\r\n\r\n\/* List *\/\r\n.custom-toc .toc-list {\r\n    list-style: none;\r\n    margin: 0;\r\n    padding: 0;\r\n}\r\n\r\n\/* Links *\/\r\n.custom-toc .toc-list li {\r\n    margin-bottom: 22px;\r\n}\r\n\r\n.custom-toc .toc-list a {\r\n    text-decoration: none;\r\n    color: #6b7a99;\r\n    font-size: 14px;\r\n    font-weight: 600;\r\n    transition: 0.3s ease;\r\n    display: inline-block;\r\n}\r\n\r\n\/* Hover Color *\/\r\n.custom-toc .toc-list a:hover {\r\n    color: #8B0000;\r\n}\r\n\r\n\/* H2 Indent *\/\r\n.custom-toc .toc-list .toc-h2 {\r\n    padding-left: 18px;\r\n    font-size: 14px;\r\n}\r\n\r\n\/* Mobile Responsive Adjustments *\/\r\n@media(max-width:768px) {\r\n    .toc-wrapper {\r\n        position: relative;\r\n        top: 0;\r\n        z-index: 1;\r\n        right: 0;\r\n        max-width: 100%;\r\n        margin-bottom: 30px;\r\n    }\r\n\r\n    .custom-toc {\r\n        max-height: none; \r\n        overflow-y: visible;\r\n    }\r\n\r\n    .custom-toc .toc-title {\r\n        font-size: 25px;\r\n    }\r\n\r\n    .custom-toc .toc-list a {\r\n        font-size: 14px;\r\n    }\r\n}\r\n<\/style>\r\n\r\n<script>\r\ndocument.addEventListener(\"DOMContentLoaded\", function () {\r\n    const tocList = document.getElementById(\"toc-list\");\r\n    const h1 = document.querySelector(\"h1\");\r\n    const h2s = document.querySelectorAll(\"h2\");\r\n\r\n    function createId(text) {\r\n        return text.toLowerCase().replace(\/[^a-z0-9]+\/g, '-');\r\n    }\r\n\r\n    if (h1) {\r\n        if (!h1.id) {\r\n            h1.id = createId(h1.innerText);\r\n        }\r\n        const li = document.createElement(\"li\");\r\n        li.innerHTML = `<a href=\"#${h1.id}\">${h1.innerText}<\/a>`;\r\n        tocList.appendChild(li);\r\n    }\r\n\r\n    h2s.forEach(h2 => {\r\n        if (!h2.id) {\r\n            h2.id = createId(h2.innerText);\r\n        }\r\n        const li = document.createElement(\"li\");\r\n        li.classList.add(\"toc-h2\");\r\n        li.innerHTML = `<a href=\"#${h2.id}\">${h2.innerText}<\/a>`;\r\n        tocList.appendChild(li);\r\n    });\r\n});\r\n<\/script>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-05f5d2f elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"05f5d2f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ecdb64d\" data-id=\"ecdb64d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5b79b60\" data-id=\"5b79b60\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fc08c85 elementor-widget elementor-widget-heading\" data-id=\"fc08c85\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">What Does Prime Factorization Mean?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a55c39b elementor-widget elementor-widget-text-editor\" data-id=\"a55c39b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Here&#8217;s the idea in plain terms, every whole number bigger than 1 is made up of prime numbers multiplied together, and there&#8217;s only ever one correct combination for any given number. Mathematicians call this the Fundamental Theorem of Arithmetic, which sounds intimidating but really just means no matter how you break a number down, you&#8217;ll always end up with the same set of primes.<\/span><\/p><p><span style=\"font-weight: 400;\">A prime number is one that can only be divided evenly by 1 and itself. 2, 3, 5, 7, 11, 13 these are primes. Something like 9 is not, because 3 divides into it. When we ask for the prime factorization of 10500, we&#8217;re asking which of these unbreakable numbers combine to build 10500 from the ground up.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c3b31db\" data-id=\"c3b31db\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-820bdf7 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"820bdf7\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-43c609a\" data-id=\"43c609a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-8a8c3de\" data-id=\"8a8c3de\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-76732ea elementor-widget elementor-widget-heading\" data-id=\"76732ea\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Method 1: The Division Method<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e9dc946 elementor-widget elementor-widget-text-editor\" data-id=\"e9dc946\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Most teachers introduce this one first, mainly because it&#8217;s hard to mess up if you go step by step.<\/span><\/p><p><b>Step 1:<\/b><span style=\"font-weight: 400;\"> Divide 10500 by the smallest prime, 2. 10500 \u00f7 2 = 5250<\/span><\/p><p><b>Step 2:<\/b><span style=\"font-weight: 400;\"> 5250 is still even, so divide by 2 again. 5250 \u00f7 2 = 2625<\/span><\/p><p><b>Step 3:<\/b><span style=\"font-weight: 400;\"> 2625 is odd now, so 2 won&#8217;t work anymore. Try the next prime, 3. 2625 \u00f7 3 = 875<\/span><\/p><p><b>Step 4:<\/b><span style=\"font-weight: 400;\"> Check 875 against 3 \u2014 add the digits (8+7+5=20), and since 20 isn&#8217;t divisible by 3, move on to 5. 875 \u00f7 5 = 175<\/span><\/p><p><b>Step 5:<\/b><span style=\"font-weight: 400;\"> 175 is still divisible by 5. 175 \u00f7 5 = 35<\/span><\/p><p><b>Step 6:<\/b><span style=\"font-weight: 400;\"> And so is 35. 35 \u00f7 5 = 7<\/span><\/p><p><b>Step 7:<\/b><span style=\"font-weight: 400;\"> 7 can&#8217;t be broken down any further it&#8217;s already prime. That&#8217;s where the division stops.<\/span><\/p><p><span style=\"font-weight: 400;\">Go back and count how many times each prime showed up along the way:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2 showed up twice<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">3 showed up once<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">5 showed up three times<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">7 showed up once<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Put together, that gives:<\/span><\/p><p><b>10500 = 2 \u00d7 2 \u00d7 3 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 7 = 2\u00b2 \u00d7 3 \u00d7 5\u00b3 \u00d7 7<\/b><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e9aca9a\" data-id=\"e9aca9a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-80f4b91 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"80f4b91\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c2cd7b6\" data-id=\"c2cd7b6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b098d0a\" data-id=\"b098d0a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d78a95a elementor-widget elementor-widget-heading\" data-id=\"d78a95a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Method 2: The Factor Tree Method\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-52bd637 elementor-widget elementor-widget-text-editor\" data-id=\"52bd637\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">If columns of division feel a bit dry, a factor tree does the same job but lets you see the number branching apart visually. It&#8217;s the version a lot of younger students find easier to follow.<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a010500<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\u00a0 \u00a0 \u00a0 \\<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5250<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\u00a0 \u00a0 \\<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02 \u00a0 \u00a0 \u00a0 2625<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\u00a0 \u00a0 \\<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03 \u00a0 \u00a0 \u00a0 875<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\u00a0 \u00a0 \\<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a05 \u00a0 \u00a0 \u00a0 175<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\u00a0 \u00a0 \\<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a05\u00a0 \u00a0 \u00a0 \u00a0 35<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\u00a0 \\<\/span><\/p><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a05\u00a0 \u00a0 \u00a0 7<\/span><\/p><p><span style=\"font-weight: 400;\">Once every branch has ended in a prime (no more splitting possible), collect all those bottom numbers: 2, 2, 3, 5, 5, 5, 7. Multiply the lot together and you land right back at:<\/span><\/p><p><b>10500 = 2\u00b2 \u00d7 3 \u00d7 5\u00b3 \u00d7 7<\/b><\/p><p><span style=\"font-weight: 400;\">It&#8217;s worth pointing out it doesn&#8217;t matter which prime you start splitting off first in a factor tree. You could begin with 5 instead of 2 and still end up with the exact same collection of primes at the end. That consistency is really the whole point of the theorem mentioned earlier.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-52d0aee\" data-id=\"52d0aee\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bf69b14 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"bf69b14\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-3c1b7e3\" data-id=\"3c1b7e3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e0f9312\" data-id=\"e0f9312\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c6a7fe3 elementor-widget elementor-widget-heading\" data-id=\"c6a7fe3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Verifying the Answer<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-545f775 elementor-widget elementor-widget-text-editor\" data-id=\"545f775\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Before you write this down as a final answer in an exam, multiply it back out and check:<\/span><\/p><p><span style=\"font-weight: 400;\">2\u00b2 = 4 4 \u00d7 3 = 12 12 \u00d7 125 (which is 5\u00b3) = 1500 1500 \u00d7 7 = 10500<\/span><\/p><p><span style=\"font-weight: 400;\">It checks out, so the factorization is correct. This habit of double checking takes ten seconds and saves you from losing marks over a small arithmetic slip somewhere in the middle of the division.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-a5dfb3d\" data-id=\"a5dfb3d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4a9110d elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"4a9110d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5e94c07\" data-id=\"5e94c07\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-62bfbc8\" data-id=\"62bfbc8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4453fa4 elementor-widget elementor-widget-heading\" data-id=\"4453fa4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Solved Examples\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-22474d0 elementor-widget elementor-widget-text-editor\" data-id=\"22474d0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>Example 1: How many prime factors does 10500 have, counting repeats?<\/b><span style=\"font-weight: 400;\"> Add up the exponents from 2\u00b2 \u00d7 3 \u00d7 5\u00b3 \u00d7 7 \u2014 that&#8217;s 2 + 1 + 3 + 1 = 7. So there are 7 prime factors in total once you count repetitions.<\/span><\/p><p><b>Example 2: How many distinct prime factors does 10500 have?<\/b><span style=\"font-weight: 400;\"> Just count the different primes involved: 2, 3, 5, and 7. That&#8217;s 4 distinct prime factors.<\/span><\/p><p><b>Example 3: How many total factors (not just prime ones) does 10500 have?<\/b><span style=\"font-weight: 400;\"> Take each exponent, add 1 to it, and multiply the results together: (2+1) \u00d7 (1+1) \u00d7 (3+1) \u00d7 (1+1) = 3 \u00d7 2 \u00d7 4 \u00d7 2 = 48 So 10500 has 48 factors altogether, including 1 and 10500 itself.<\/span><\/p><p><b>Example 4: Is 10500 a perfect square?<\/b><span style=\"font-weight: 400;\"> For a perfect square, every exponent in the factorization needs to be even. Here, both 3 and 7 have an exponent of 1, which is odd \u2014 so no, 10500 isn&#8217;t a perfect square.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0271da4\" data-id=\"0271da4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-aa260c4 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"aa260c4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b1d4928\" data-id=\"b1d4928\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-fcee4e7\" data-id=\"fcee4e7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0072bcb elementor-widget elementor-widget-heading\" data-id=\"0072bcb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Where This Is Actually Used<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bfedfe2 elementor-widget elementor-widget-text-editor\" data-id=\"bfedfe2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">It&#8217;s fair to ask why any of this matters beyond a worksheet. A few honest reasons:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>HCF and LCM problems<\/b><span style=\"font-weight: 400;\"> get a lot faster once you already have the prime factorization of both numbers written out you&#8217;re basically just comparing lists.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Simplifying fractions<\/b><span style=\"font-weight: 400;\"> is easier when you can spot common prime factors in the numerator and denominator and cancel them directly.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Square roots and cube roots<\/b><span style=\"font-weight: 400;\"> become obvious once you notice which primes repeat, and how many times.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Divisibility,<\/b><span style=\"font-weight: 400;\">\u00a0once you know 10500 = 2\u00b2 \u00d7 3 \u00d7 5\u00b3 \u00d7 7, you can instantly tell which numbers divide into it evenly, without testing each one by hand.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e46e0a1\" data-id=\"e46e0a1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ba23fc7 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"ba23fc7\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-d80bdb4\" data-id=\"d80bdb4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5f038ba\" data-id=\"5f038ba\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-28dea06 elementor-widget elementor-widget-heading\" data-id=\"28dea06\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Quick Recap<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-942d521 elementor-widget elementor-widget-text-editor\" data-id=\"942d521\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<table><tbody><tr><td><p><b>Detail<\/b><\/p><\/td><td><p><b>Value<\/b><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Number<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">10500<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Prime Factorization<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2\u00b2 \u00d7 3 \u00d7 5\u00b3 \u00d7 7<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Distinct Prime Factors<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2, 3, 5, 7<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Total Prime Factors (with repetition)<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">7<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Total Factors<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">48<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Perfect Square?<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">No<\/span><\/p><\/td><\/tr><\/tbody><\/table>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-a4f922a\" data-id=\"a4f922a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3558c71 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"3558c71\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-2689c07\" data-id=\"2689c07\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6ac7c47\" data-id=\"6ac7c47\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0930a67 elementor-widget elementor-widget-heading\" data-id=\"0930a67\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d8ed35d elementor-widget elementor-widget-text-editor\" data-id=\"d8ed35d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Working out the <strong>prime factorization of 10500<\/strong> isn&#8217;t really about memorizing an answer it&#8217;s about knowing how to break any number down, one prime at a time, until nothing&#8217;s left to divide. Whether you get there through the division method or a factor tree, you&#8217;ll always land on the same result: 2\u00b2 \u00d7 3 \u00d7 5\u00b3 \u00d7 7. That&#8217;s the whole point of prime factorization it&#8217;s consistent, it&#8217;s checkable, and once you&#8217;ve done it a few times, numbers like 10500 stop feeling like a puzzle and start feeling like a routine calculation. The real payoff shows up later, when you&#8217;re simplifying fractions or finding HCF and LCM in seconds because you already know exactly what a number is built from.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-850559e\" data-id=\"850559e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d1368b2 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"d1368b2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-48bcbf6\" data-id=\"48bcbf6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-cdca626\" data-id=\"cdca626\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c976e46 elementor-widget elementor-widget-heading\" data-id=\"c976e46\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Frequently Asked Questions\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ac54608 elementor-widget elementor-widget-accordion\" data-id=\"ac54608\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1801\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1801\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">What is the prime factorization of 10500?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1801\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1801\"><p><span style=\"font-weight: 400;\">2\u00b2 \u00d7 3 \u00d7 5\u00b3 \u00d7 7<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1802\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-1802\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Is 10500 a prime number?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1802\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-1802\"><p><span style=\"font-weight: 400;\">No, it&#8217;s a composite number, since several numbers other than 1 and itself divide into it evenly.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1803\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-1803\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">What are the distinct prime factors of 10500?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1803\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-1803\"><p><span style=\"font-weight: 400;\">2, 3, 5, and 7<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1804\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-1804\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">How many total factors does 10500 have?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1804\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-1804\"><p><span style=\"font-weight: 400;\">48, including 1 and 10500<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1805\" class=\"elementor-tab-title\" data-tab=\"5\" role=\"button\" aria-controls=\"elementor-tab-content-1805\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Division method or factor tree which one should I use?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1805\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"5\" role=\"region\" aria-labelledby=\"elementor-tab-title-1805\"><p><span style=\"font-weight: 400;\">Whichever one clicks for you. They&#8217;ll always give the same answer. Division tends to be quicker once you&#8217;re comfortable with it, but a factor tree is often easier to follow the first few times you&#8217;re learning the concept.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"What is the prime factorization of 10500?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">2\\u00b2 \\u00d7 3 \\u00d7 5\\u00b3 \\u00d7 7<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"Is 10500 a prime number?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">No, it&#8217;s a composite number, since several numbers other than 1 and itself divide into it evenly.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"What are the distinct prime factors of 10500?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">2, 3, 5, and 7<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"How many total factors does 10500 have?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">48, including 1 and 10500<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"Division method or factor tree which one should I use?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Whichever one clicks for you. They&#8217;ll always give the same answer. Division tends to be quicker once you&#8217;re comfortable with it, but a factor tree is often easier to follow the first few times you&#8217;re learning the concept.<\\\/span><\\\/p>\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0fba7bb\" data-id=\"0fba7bb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Prime Factorization of 10500 : Step-by-Step Method with Solved Examples The prime factorization of 10500 is 2\u00b2 \u00d7 3 \u00d7 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":6765,"comment_status":"open","ping_status":"open","sticky":false,"template":"rttpg_full_width","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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