# 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

 1! = 1 × 1 = 1
 2! = 2 × 1 = 2
 3! = 3 × 2 × 1 = 6
 4! = 4 × 3 × 2 × 1 = 24
 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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