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

$n!=1\cdot 2\cdot 3\cdots (n-2)\cdot (n-1)\cdot n$

for $n\ge 1$.

The same written as mathmatical product

$n!=\prod _{i=1}^{n}i.$

and as recurrence relation

$n!=n\cdot (n-1)!$

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