What is a Factorial?
Definition: A factorial of a positive integer n, denoted as n!, is the product of all positive integers less than or equal to n.
n! = n × (n-1) × (n-2) × ... × 2 × 1
Special Case: By definition, 0! = 1 (this is a mathematical convention that makes many formulas work correctly).
Examples
5! = 5 × 4 × 3 × 2 × 1 = 120
4! = 4 × 3 × 2 × 1 = 24
3! = 3 × 2 × 1 = 6
2! = 2 × 1 = 2
1! = 1
0! = 1 (by definition)
Interactive Factorial Calculator
Click "Calculate Factorial" to see the result!
Where Are Factorials Used?
Factorials are important in many areas of mathematics:
- Combinatorics: Counting arrangements and combinations
- Probability: Calculating probabilities of events
- Calculus: Taylor series expansions
- Statistics: Various statistical formulas
Quick Facts
- Factorials grow very quickly! 10! = 3,628,800
- The factorial of negative numbers is undefined
- The symbol "!" was introduced by Christian Kramp in 1808
- 20! is over 2 quintillion!