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Number Notation: Factorial Operation

Document Reference: TN201106002 - Rev: 4.19 - Last Update: 30-07-2016 18:06 GMT - Downloaded: 17-Sep-2019 19:38 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! =nk                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 × 12 × 12!1!

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