Trailing zeros in 65 factorial = 15

Quick Answer: 15 trailing zeros in 65!
Legendre's Formula: Count factors of 5 in 65! ⌊65/5⌋ = 13 + ⌊65/25⌋ = 2 = 15

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Trailing Zeros in 65!

Trailing zeros in 65! = 15

How 65! is calculated

The number of trailing zeros in 65! is 15.
The number of digits in 65 factorial is 91.
The factorial of 65 is calculated, through its definition, this way:
65! = 65 • 64 • 63 • 62 • 61 ... 3 • 2 • 1

Exact value of 65!

65! = 8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000

Nearby Factorials

n	n!	Digits	Trailing Zeros
60!	83209871...0000	82	14
61!	50758021...0000	84	14
62!	31469973...0000	86	14
63!	19826083...0000	88	14
64!	12688693...0000	90	14
65!	82476505...0000	91	15
66!	54434493...0000	93	15
67!	36471110...0000	95	15
68!	24800355...0000	97	15
69!	17112245...0000	99	15
70!	11978571...0000	101	16

More factorial calculations

Here you can find answers to questions like: What is the number of zeros on the end of 65 factorial What is the factorial of 65? What is the last digits of factorial of 65? How many trailing zeros in 65 factorial? How many digits are there in 65 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 65 factorial?

There are 15 trailing zeros in 65!. This is calculated using Legendre's formula: count how many times 5 divides into 65, 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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