Factorial Calculator
Factorial Calculator Until 10,000
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
What is a factorial?
A factorial (written as n!) is the product of all positive integers less than or equal to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1.
How do you calculate trailing zeros in a factorial?
Use Legendre's formula: count factors of 5 by calculating ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + ... The sum gives the number of trailing zeros in n!.
What is the largest factorial this calculator can compute?
This calculator can compute factorials up to 10,000! It displays the exact value, number of digits, and trailing zeros for any factorial in this range.
Factorial Calculator
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Popular Factorial Calculations
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Trailing Zeros in Factorials
Find how many trailing zeros are in n! using Legendre's formula:
Digits in Factorials
Find how many digits are in n! using Stirling's approximation: