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What Are the Factors of 72? Complete List, Pairs and Prime Factorization

I remember when I was a kid I used to get stuck on math problems. If you are like me and you are trying to figure out what the factors of 72 are you are in the place. I will explain it in a way that’s easy to understand. I do not want to confuse you with words or complicated ideas. I will just tell you what the factors of 72 are and how they work.

By the time you finish reading this you will know all the factors of 72. You will understand how they pair up with each other. You will also understand the factorization of 72.. The best part is you will be able to figure out the factors of any other number on your own.

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    Quick Answer: The Factors of 72

    The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72. There are twelve factors in total. Each one of them can divide 72 evenly without leaving a remainder.
    What Does a Factor Actually Mean

    A factor is a number that can divide another number completely. So when we ask what the factors of 72 are we are asking which whole numbers can divide 72 without leaving a remainder. For example if we divide 72 by 8 we get 9. Since there is no remainder both 8 and 9 are factors of 72.. If we try dividing 72 by 5 we get 14.4. Since that is not a number 5 is not a factor of 72.

    This is different from a multiple. Multiples of 72 are numbers that we get by multiplying 72 by numbers. For example 72, 144, 216 and so on. Factors of 72 are numbers that can divide 72 evenly. They are always equal to or smaller than 72.. There are only a limited number of them.

    Complete List of Factors of 72

    I think it helps to see how we get the factors of 72. So lets go through the list. When we divide 72 by 1 we get 72. That is a number so 1 is a factor of 72. When we divide 72 by 2 we get 36. That is a number so 2 is a factor of 72. When we divide 72 by 3 we get 24. That is a number so 3 is a factor of 72. We keep going like this until we have checked all the numbers. The factors of 72 are 1 2, 3 4 6 8 9 12 18 24 36 and 72.

    You might notice that after a point the numbers start repeating. That is because the factors of 72 pair up with each other. I will explain that in the section.

    Factor Pairs of 72

    A factor pair is two numbers that multiply together to give 72. Each factor of 72 has a partner. When we pair them up it is a way to check that we have not missed any factors. The factor pairs of 72 are: 1 and 72, 2 and 36 3 and 24 4 and 18 6 and 12 and 8 and 9. There are six factor pairs in total. If we multiply each pair we get 72.

    Negative Factor Pairs of 72

    If we are working with numbers we need to know that 72 also has negative factor pairs. This is because a negative number multiplied by another number gives a positive result. The negative factor pairs of 72 are: -1. -72, -2 And -36, -3 and -24, -4 and -18 -6 and -12 and -8 and -9. Most of the time we only need to worry about factors.. It is good to know about negative factors too.

    Prime Factorization of 72

    Prime factorization is a way of breaking down a number into its parts. We keep dividing the number by numbers until we cannot divide anymore. The prime factorization of 72 is 2 x 2 x 2 x 3 x 3. We can write this in a way as 2^3 x 3^2. This is like a code that only works for 72.

    Prime Factor Tree of 72

    If you like pictures a prime factor tree can help you understand the factors of 72. We start with 72 at the top. Then we branch down into smaller numbers. The prime factor tree of 72 shows us that 72 = 8 x 9. Then 8 = 2 x 4 and 4 = 2 x 2.. 9 = 3 X 3. This gives us the result as the prime factorization.

    Is 72 a Prime Number or a Composite Number

    72 is a number. It is not a number. A prime number only has two factors: 1 and itself.. 72 Has twelve factors. That means it is a number. Composite numbers like 72 have factor pairs. That is why they are useful in math problems.

    How Many Factors Does 72 Have

    72 has twelve factors. We can figure this out from the factorization. We take the exponents which’re 3 and 2 and add 1 to each of them. Then we multiply the results together. This gives us 4 x 3 = 12. This confirms that 72 has twelve factors.

    Common Factors of 72 With Other Numbers

    Understanding the factors of 72 is useful when we compare it to numbers. For example lets look at 72 and 36. The factors of 36 are 1 2, 3 4 6 9 12, 18 and 36. All of these numbers are also factors of 72. That is because 36 is a factor of 72. This is useful, in math problems that involve common factor and least common multiple.

    Now look at 72 and 48. The factors of 48 are 1 2, 3 4 6 8 12 16, 24 and 48. When you compare that list to the factors of 72 the shared numbers are 1, 2 3 4 6 8, 12 and 24. This makes the common factor between 72 and 48 equal to 24.

    Lets look at another example, 72 and 90. The factors of 90 are 1 2, 3 5 6 9 10 15 18 30, 45 and 90. Comparing the two lists shows the common factors are 1, 2 3 6, 9 and 18. This makes the greatest common factor between 72 and 90 equal to 18.

    Why Learning the Factors of 72 Matters in Real Life

    I know this can seem like another thing you learn in school but understanding the factors of 72 and understanding how to find factors in general actually helps in everyday life.

    Think about splitting things into groups. If you have 72 things. You need to divide them among a group of people or into boxes knowing the factors of 72 tells you which group sizes will work perfectly whether that is groups of 8, 9, 12 or 24.

    It also helps when you are simplifying fractions. A fraction like 24 over 72 becomes much easier to simplify once you see that 24 is a factor of 72 and the fraction reduces down to one third.

    The factors of 72 show up in scheduling and measurement. 72 Can be divided evenly into useful chunks and that is why you see this number in recipes, layouts and time based planning.

    To be honest students who get comfortable working with factors tend to do better in fractions, ratios and algebra later on because they already have a good sense of numbers.

    Conclusion

    To bring it all together what are the factors of 72? They are 1, 2 3 4 6 8 9, 12 18 24 36 and 72 twelve numbers that divide into 72 without leaving anything arranged into six factor pairs, all built from the prime numbers 2 and 3. Once you understand how to find the factors of 72 you can apply that process to any number, whether it is, for a homework assignment, a quick calculation or helping someone else understand it the same way I have hopefully just helped you understand the factors of 72.

    Frequently Asked Questions

     The complete list is 1, 2 3 4 6 8 9 12 18 24 36 and 72.

     It is 2 times 2 times 2 times 3 times 3 or written with exponents 2 cubed times 3 squared.

    There are six factor pairs of 72 which’re 1 and 72 2 and 36 3 and 24 4 and 18 6 and 12 and 8 and 9.

    No it is not. A perfect square always has a number of total factors and since 72 has twelve factors, which is an even number that confirms it cannot be a perfect square. The nearest perfect squares to 72 are 64, which’s 8 squared and 81 which is 9 squared.

    The greatest common factor is found between two or more numbers, not for a number. For example the greatest common factor between 72 and 48 is 24.

    72 is a number since it can be divided evenly by 2 and that is also why the number 2 appears three times in its prime factorization.

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