Factorial Table
This page provides a clean factorial (n!) lookup table for commonly used integers. Factorials grow very quickly, so having a reference table is useful for quick checks in combinatorics, probability, and discrete mathematics.
Factorial Calculator
Enter a non-negative integer to find its factorial (n!).
6!720
What is a factorial?
The factorial of a non-negative integer n (written as n!) is the product of all positive integers less than or equal to n:
- 0! = 1
- n! = n × (n − 1) × (n − 2) × … × 2 × 1 for n ≥ 1
Factorials appear frequently in formulas such as permutations and combinations. For example, the number of ways to choose k items from n is: C(n, k) = n! / (k! (n − k)!).
Factorial Table (n!)
Use the table below to look up exact values of n! for common integers. Values increase rapidly, so for larger n, scientific notation is typically used in applied settings.
| n | n! | Expanded form |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 1 | 1 |
| 2 | 2 | 2 × 1 |
| 3 | 6 | 3 × 2 × 1 |
| 4 | 24 | 4 × 3 × 2 × 1 |
| 5 | 120 | 5 × 4 × 3 × 2 × 1 |
| 6 | 720 | 6 × 5 × 4 × 3 × 2 × 1 |
| 7 | 5,040 | 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 8 | 40,320 | 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 9 | 362,880 | 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 10 | 3,628,800 | 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 11 | 39,916,800 | 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 12 | 479,001,600 | 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 13 | 6,227,020,800 | 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 14 | 87,178,291,200 | 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 15 | 1,307,674,368,000 | 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 16 | 20,922,789,888,000 | 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 17 | 355,687,428,096,000 | 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 18 | 6,402,373,705,728,000 | 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 19 | 121,645,100,408,832,000 | 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
| 20 | 2,432,902,008,176,640,000 | 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 |
Common uses of factorials
- Permutations: number of ways to arrange n distinct items is n!.
- Combinations: choosing k items from n uses factorials in C(n, k).
- Probability: counting outcomes in discrete sample spaces often relies on factorials.
- Series expansions: factorials appear in denominators (e.g., exponential series).