# 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.

## Contents

## Definition

A factorial is defined by the product

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

for [math]n ≥ 1[/math].

The same written as mathmatical product

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

and as recurrence relation

- [math] 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