Trailing zeros in 100 factorial = 24

Quick Answer: 24 trailing zeros in 100!
Legendre's Formula: Count factors of 5 in 100! ⌊100/5⌋ = 20 + ⌊100/25⌋ = 4 = 24

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Trailing Zeros in 100!

Trailing zeros in 100! = 24

How 100! is calculated

The number of trailing zeros in 100! is 24.
The number of digits in 100 factorial is 158.
In scientific notation: 100! ≈ 9.332621 × 10¹⁵⁷
The factorial of 100 is calculated, through its definition, this way:
100! = 100 • 99 • 98 • 97 • 96 ... 3 • 2 • 1

Exact value of 100!

100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

Nearby Factorials

n	n!	Digits	Trailing Zeros
95!	10329978...0000	149	22
96!	99167793...0000	150	22
97!	96192759...0000	152	22
98!	94268904...0000	154	22
99!	93326215...0000	156	22
100!	93326215...0000	158	24
101!	94259477...0000	160	24
102!	96144667...0000	162	24
103!	99029007...0000	164	24
104!	10299016...0000	167	24
105!	10813967...0000	169	25

More factorial calculations

Here you can find answers to questions like: What is the number of zeros on the end of 100 factorial What is the factorial of 100? What is the last digits of factorial of 100? How many trailing zeros in 100 factorial? How many digits are there in 100 factorial? Use the factorial calculator above to find the factorial of any natural between 0 and 10,000.

What is factorial?

Definition of factorial

The factorial is a quantity defined for any integer n greater than or equal to 0.

The factorial is the product of all integers less than or equal to n but greater than or equal to 1. The factorial value of 0 is, by definition, equal to 1. For negative integers, factorials are not defined. The factorial can be seen as the result of multiplying a sequence of descending natural numbers (such as 3 × 2 × 1).

The factorial symbol is the exclamation mark (!).

The factorial formula

If n is a natural number greater than or equal to 1, then

n! = n x (n - 1) x (n - 2) x (n - 3) ... 3 x 2 x 1

If n = 0, then n! = 1, by convention.

Example: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Shortcut to find trailing zeros in a factorial

Trailing zeros are a sequence of zeros in the decimal representation of a number, after which no other digits follow. This video shows how to find the trailing zeros of a factorial easily.

Table of factorials until 30

n	n!
1!	1	#
2!	2	#
3!	6	#
4!	24	#
5!	120	#
6!	720	#
7!	5040	#
8!	40320	#
9!	362880	#
10!	3628800	#
11!	39916800	#
12!	479001600	#
13!	6227020800	#
14!	87178291200	#
15!	1307674368000	#
16!	20922789888000	#
17!	355687428096000	#
18!	6402373705728000	#
19!	121645100408832000	#
20!	2432902008176640000	#
21!	51090942171709440000	#
22!	1124000727777607680000	#
23!	25852016738884976640000	#
24!	620448401733239439360000	#
25!	15511210043330985984000000	#
26!	403291461126605635584000000	#
27!	10888869450418352160768000000	#
28!	304888344611713860501504000000	#
29!	8841761993739701954543616000000	#
30!	265252859812191058636308480000000	#

Frequently Asked Questions

How many trailing zeros are in 100 factorial?

There are 24 trailing zeros in 100!. This is calculated using Legendre's formula: count how many times 5 divides into 100, then 25, then 125, and so on, adding up all the quotients.

What is Legendre's formula?

Legendre's formula calculates the number of trailing zeros in n! by summing ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + ... until the quotient becomes 0. Each trailing zero comes from a factor of 10, which requires one factor of 2 and one factor of 5.

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