What Is the Factorial of 300? Value, Number of Digits and Trailing Zeros

You want to know what is the factorial of 300, so here it is. Multiply every whole number from 1 up to 300:

300! = 300 × 299 × 298 × … × 3 × 2 × 1

That gives you roughly 3.06 × 10^614. The number has 615 digits, and the last 74 of them are zeros.

Property	Value
Notation	300!
Approximate value	≈ 3.06 × 10^614
Total digits	615
Trailing zeros	74
Digits before the trailing zeros	541

Honestly, nobody searches this because they want to read 615 digits. Most people are after one of three things: how big it is, how many digits it has, or how many zeros are stuck on the end. That last one pops up in school tests and aptitude exams all the time. I’ll walk through all three, and I’ll show the working so you never have to just trust me.

☰ Table of Contents

Finding the Factorial of 300

Haven’t thought about factorials since school? Totally fine. A factorial just means “take this number and multiply it by every whole number below it.” The symbol is an exclamation mark, which feels about right once you see how quickly the numbers explode.

4! = 4 × 3 × 2 × 1 = 24
6! = 720
10! = 3,628,800
20! = 2,432,902,008,176,640,000

Here’s a quirk that catches people off guard: 0! equals 1. It feels like a cheat, but it’s what keeps the permutation and combination formulas working.

Look at how fast that escalates. By 20! you’re already at 19 digits. By 300!, your phone calculator has packed up and left.

Why do factorials matter? Because they count arrangements. Any time you ask “in how many different orders can I put these things?”, a factorial is lurking nearby. That covers probability, statistics, and the series you meet in calculus.

What Is the Factorial of 300? The Value in Scientific Notation

About 3.06 × 10^614. That’s a 3 followed by 614 more digits.

Hard to picture, right? Try this. Scientists estimate the observable universe contains around 10^80 atoms. Raise that to the seventh power and you get 10^560. 300! still leaves that in the dust. Nothing in the physical world comes anywhere near it.

Or think about it like this. Get 300 people in a room and ask them to line up in every possible order. That’s 300! different lineups. Even if a computer listed a trillion of them every second since the Big Bang, it would barely have scratched the surface.

How Many Digits Does 300! Have you?

Here’s something handy: you can count the digits without writing the number out at all.

For any positive whole number N, the digit count is ⌊log₁₀(N)⌋ + 1. For factorials, a result called Stirling’s approximation gives a really good estimate of that logarithm. The shortcut built from it is known as Kamenetsky’s formula:

Digits = ⌊ n × log₁₀(n / e) + ½ × log₁₀(2πn) ⌋ + 1

It looks intimidating, but it’s really just two small calculations added together. With n = 300:

300 × log₁₀(300 / 2.71828) ≈ 300 × 2.04283 ≈ 612.85
½ × log₁₀(2π × 300) ≈ ½ × 3.27530 ≈ 1.64
Add them: 612.85 + 1.64 ≈ 614.49
Round down and add 1: 614 + 1 = 615 digits

Want a second opinion? Add up log₁₀(1) + log₁₀(2) + … + log₁₀(300) the slow way. You’ll land on about 614.49 again, which sits between 614 and 615, so the answer is 615 digits. Two different roads, same destination. Always a good sign.

How Many Trailing Zeros Does 300! Have you?

This is the one that trips people up, so let’s slow down and go step by step.

A trailing zero comes from a factor of 10, and every 10 is built from one 2 and one 5. Inside a factorial, 2s are everywhere, since every even number brings at least one. But 5s are far scarcer. That makes the 5s the bottleneck. Count the 5s and you’ve counted the zeros.

The formula, usually credited to Legendre, goes like this:

Trailing zeros = ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + ⌊n/625⌋ + …

For 300:

⌊300 / 5⌋ = 60
⌊300 / 25⌋ = 12
⌊300 / 125⌋ = 2
⌊300 / 625⌋ = 0, so we stop

60 + 12 + 2 = 74 trailing zeros.

Why do we keep dividing by 25 and 125?

This is exactly where most people slip. Some numbers sneak in more than one 5.

Every multiple of 5 gives you one. But 25 is 5 × 5, so numbers like 25, 50, and 75 smuggle in a second 5. And 125 is 5 × 5 × 5, so 125 and 250 bring a third. Each new term in the formula catches the 5s the last one missed.

The same thing, in everyday words

Between 1 and 300, there are 60 multiples of 5. Twelve of those are also multiples of 25, and two of those are multiples of 125. Stack the layers and you get 60 + 12 + 2 = 74 fives. There are plenty of 2s to pair them with, so that’s 74 tens, which means 74 trailing zeros. Simple as that.

Want the Exact Number? Let a Computer Handle It

If you really do want all 615 digits, please don’t try it by hand. Python handles huge integers with no special setup:

import math

n = 300

f = math.factorial(n)

print(f) # full exact value

print(len(str(f))) # 615 digits

print(len(str(f)) – len(str(f).rstrip(‘0’))) # 74 trailing zeros

WolframAlpha and online big-number factorial calculators work well too. A spreadsheet’s FACT function will give you an answer, but in scientific notation, because spreadsheets only keep about 15 significant digits. And your phone’s calculator? It’ll most likely show an error or “infinity.”

Quick tip: if you just need the size for a probability or combinatorics problem, 3.06 × 10^614 is almost always enough.

How 300! Compares to Other Factorials

Seeing 300! next to a few of its neighbors makes the growth easier to feel:

n	Digits in n!	Trailing zeros
10	7	2
50	65	12
100	158	24
200	375	49
300	615	74
500	1,135	124
1,000	2,568	249

The zeros climb at roughly n/4, a steady, almost straight-line rise. The digit count speeds up, because every new number you multiply by adds a little more than the last one did.

Where Does 300! Actually Come Up?

You’ll almost never need the full number, but the idea behind it turns up in lots of places:

Permutations: The number of ways to arrange 300 different items is exactly 300!.
Combinations and probability: Expressions like C(300, k) = 300! / (k! × (300 − k)!) have factorials on top and bottom. Giant factorials often cancel out, so you can solve these without ever calculating 300! in full.
Computer science: Factorials are a classic test of big-integer math, recursion, and algorithm speed.
Statistics: Binomial and Poisson distributions both rely on them.
Exams: “How many zeros are at the end of 300!” shows up in school olympiads, aptitude tests, and entrance papers. Now you know the answer is 74.

Mistakes Almost Everyone Makes

Counting only multiples of 5. That gives you 60, not 74. Don’t forget the multiples of 25 and 125.
Mixing up digits and trailing zeros. 300! has 615 digits in total, but only 74 zeros at the end. There are zeros scattered through the middle too.
Trusting a basic calculator. Most will overflow or round the result. Use a big-number tool for the exact value.
Not knowing when to stop. Once a division gives 0 (here, 300/625), every later term is 0 as well.
Confusing 300! with 300². One multiplies 300 numbers together. The other is just 300 × 300 = 90,000. Big difference.

A Shortcut That Works on Any Factorial

Once the 300! example clicks, you can handle almost any factorial question in two steps:
1. For trailing zeros: divide n by 5, 25, 125, and so on. Ignore the remainders and add up the results.
2. For digits: use the Kamenetsky formula, or add the base-10 logs of 1 through n.
Try it on 150!: ⌊150/5⌋ + ⌊150/25⌋ + ⌊150/125⌋ = 30 + 6 + 1 = 37 trailing zeros. After a little practice, you’ll finish these in under a minute.

Conclusion

300! ≈ 3.06 × 10^614
It has 615 digits
It ends in 74 trailing zeros
Two simple formulas give you the digit count and the zeros without calculating the whole number
For the exact value, use Python, WolframAlpha, or another big-integer tool

Want some practice? Try the trailing-zeros method on 500! (124 zeros) or 1000! (249 zeros), then check yourself against the table above. Do it twice and it’ll stick for good.

Frequently Asked Questions

What is the factorial of 300?

It’s every whole number from 1 to 300 multiplied together. The result is about 3.06 × 10^614, and it has 615 digits.

Can I see the exact value of 300!?

Yes. Python or WolframAlpha will print it instantly. Working it out by hand just isn’t realistic.

Is 300! divisible by 10^74?

Yes. With exactly 74 trailing zeros, it divides evenly by 10^74 but not by 10^75.

What's the formula for trailing zeros in a factorial?

Add ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ and keep going until a division gives 0.

Why does 300! have so many digits?

Almost every number you multiply by is bigger than 10, and each of those steps adds at least one digit to the total. With nearly 300 steps, the digits pile up fast.