# Number Notation: Factorial Operation

Document Reference: TN201106002 - Rev: 4.19 - Last Update: 30-07-2016 18:06 GMT - Downloaded: 23-Apr-2021 07:28 GMT

## Using the factorial notation, `n!`

(pronounced "n factorial") is defined as the product of all the positive natural numbers up to a given number `n`

.

Please note that the factorial function can also be defined for non-integer values using more advanced mathematics. This is not covered in this section.

### Notation And Definition

n! = | n | k | | | 1! = 1 × 1 = 1 | | | 0! = 1 ^{1)} |

Π |

k=1 |

^{1)}By convention that the product of no numbers at all is 1.

### Worked Examples

5! = 5 × 4 × 3 × 2 × 1 = 120 |

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 |

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5 040 |

Note: As long as `n > 1`

, we can assume that `n! = n(n-1)!`

e.g.:

8! = 8 × (8 - 1)! = 8 × 7! = 8 × 5 040 = 40 320 |

#### Fractions

4! | = | 4 × 3 × 2 × 1 | = | 4 × 3 × 2 × 1 | = | 4 × 3 | = 12 | | | 4! | ≠ | 2! |

2! | 2 × 1 | 2 × 1 | 2! | 1! |

This website uses cookies to give you the best experience on our website, to personalise content and to analyse our website traffic. Some cookies may have been set already. To find out more about our use of cookies you can visit our Privacy Statement. By browsing this website, you agree to our use of cookies.

Hide this message