Factorial

The factorial of a natural number , denoted by , is the product of all natural numbers smaller than or equal to :

The expression is read " factorial". Furthermore, by convention:

The factorial of is also equal to the number of possible ways of ordering objects.

An in-depth explanation of factorials can be found in the lecture entitled Permutations.

Examples

As an example, the factorial of 6 is:

It is also frequent to encounter ratios of factorials, which can be computed by simplifying the common terms. For example:

Generalization

The concept of factorial can also be extended to non-integer numbers, using the Gamma function.

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