Trailing zeros in 52 factorial = 12

Quick Answer: 12 trailing zeros in 52!
Legendre's Formula: Count factors of 5 in 52! ⌊52/5⌋ = 10 + ⌊52/25⌋ = 2 = 12

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Trailing Zeros in 52!

Trailing zeros in 52! = 12

How 52! is calculated

The number of trailing zeros in 52! is 12.
The number of digits in 52 factorial is 68.
The factorial of 52 is calculated, through its definition, this way:
52! = 52 • 51 • 50 • 49 • 48 ... 3 • 2 • 1

Exact value of 52!

52! = 80658175170943878571660636856403766975289505440883277824000000000000

Nearby Factorials

n	n!	Digits	Trailing Zeros
47!	25862324...0000	60	10
48!	12413915...0000	62	10
49!	60828186...0000	63	10
50!	30414093...0000	65	12
51!	15511187...0000	67	12
52!	80658175...0000	68	12
53!	42748832...0000	70	12
54!	23084369...0000	72	12
55!	12696403...0000	74	13
56!	71099858...0000	75	13
57!	40526919...0000	77	13

More factorial calculations

Here you can find answers to questions like: What is the number of zeros on the end of 52 factorial What is the factorial of 52? What is the last digits of factorial of 52? How many trailing zeros in 52 factorial? How many digits are there in 52 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 52 factorial?

There are 12 trailing zeros in 52!. This is calculated using Legendre's formula: count how many times 5 divides into 52, 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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