Factorial Calculator
Calculate factorials (n!) for any positive integer. Supports large numbers up to 170!. Free online factorial calculator.
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Result
Common Factorials
| n | n! |
|---|---|
| 0 | 1 |
| 1 | 1 |
| 2 | 2 |
| 3 | 6 |
| 4 | 24 |
| 5 | 120 |
| 6 | 720 |
| 7 | 5,040 |
| 8 | 40,320 |
| 9 | 362,880 |
| 10 | 3,628,800 |
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What Is a Factorial?
The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It is denoted by n! and defined as:
By convention, 0! = 1. This convention makes many mathematical formulas work correctly, especially in combinatorics where it represents the number of ways to arrange zero items (exactly one way: do nothing).
Factorials grow extremely fast. While 5! is only 120, 10! is 3,628,800 and 20! is about 2.4 quintillion. This rapid growth is why they are so useful for counting large numbers of permutations and combinations.
Factorials appear throughout mathematics and computer science, from calculating probabilities and binomial coefficients to power series expansions in calculus.