Trailing zeros in 116 factorial = 27

Quick Answer: 27 trailing zeros in 116!
Legendre's Formula: Count factors of 5 in 116! ⌊116/5⌋ = 23 + ⌊116/25⌋ = 4 = 27

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Trailing Zeros in 116!

Trailing zeros in 116! = 27

How 116! is calculated

The number of trailing zeros in 116! is 27.
The number of digits in 116 factorial is 191.
In scientific notation: 116! ≈ 3.393108 × 10¹⁹⁰
The factorial of 116 is calculated, through its definition, this way:
116! = 116 • 115 • 114 • 113 • 112 ... 3 • 2 • 1

Exact value of 116!

116! = 33931086844518982011982560935885732032396635556994207701963662088123265314176330336254535971207181169698868584991941607780111073928236261199604691797570505851011072000000000000000000000000000

Nearby Factorials

n	n!	Digits	Trailing Zeros
111!	17629525...0000	181	26
112!	19745068...0000	183	26
113!	22311927...0000	185	26
114!	25435597...0000	187	26
115!	29250936...0000	189	27
116!	33931086...0000	191	27
117!	39699371...0000	193	27
118!	46845258...0000	195	27
119!	55745857...0000	197	27
120!	66895029...0000	199	28
121!	80942985...0000	201	28

More factorial calculations

Here you can find answers to questions like: What is the number of zeros on the end of 116 factorial What is the factorial of 116? What is the last digits of factorial of 116? How many trailing zeros in 116 factorial? How many digits are there in 116 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 116 factorial?

There are 27 trailing zeros in 116!. This is calculated using Legendre's formula: count how many times 5 divides into 116, 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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