Factorial number

In mathematics symbolized by placing the "!" (known as the exclamation mark or bang) after a number, it represents multiplying a number by all whole numbers smaller than it.

Definition

A factorial is defined by the product

[math]\displaystyle{ n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n }[/math]

for [math]\displaystyle{ n \ge 1 }[/math].

The same written as mathmatical product

[math]\displaystyle{ n! = \prod_{i = 1}^n i. }[/math]

and as recurrence relation

[math]\displaystyle{ n! = n \cdot (n-1)! }[/math]

Examples

5! = 5 * 4 * 3 * 2 * 1 = 120

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800

See also

• Factorial prime
• Multifactorial number

External links

• Factorial