Factorial Calculator
Calculate Factorials, Permutations & Combinations
Calculate factorials (n!), permutations (nPr), and combinations (nCr) with detailed step-by-step solutions and mathematical properties.
Factorial (n!)
Enter a non-negative integer (0-170)
Permutation & Combination
Quick Facts
- • 0! = 1 (by definition)
- • 1! = 1
- • n! grows very rapidly
- • 10! = 3,628,800
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About Factorials
A factorial is the product of all positive integers less than or equal to a given number. It is denoted by n! and is fundamental in combinatorics, probability, and algebra.
For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow extremely fast - 10! is already over 3 million!
Applications:
- Counting permutations and arrangements
- Probability calculations
- Combinatorial problems
- Series expansions in calculus
Formulas
Factorial:
n! = n × (n-1) × (n-2) × ... × 2 × 1
0! = 1 (by definition)
Permutation:
nPr = n! / (n-r)!
Combination:
nCr = n! / (r! × (n-r)!)
Common Factorial Values
| n | n! | Digits |
|---|---|---|
| 0 | 1 | 1 |
| 5 | 120 | 3 |
| 10 | 3,628,800 | 7 |
| 15 | 1,307,674,368,000 | 13 |
| 20 | 2,432,902,008,176,640,000 | 19 |