# Number Notation: Factorial Operation

Document Reference: TN201106002 - Rev: 4.19 - Last Update: 30-07-2016 18:06 GMT - Downloaded: 24-Sep-2023 18:49 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! |

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