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The factorial function of natural numbers is a function that takes a natural number and returns the product of all nonzero naturals less than or equal to that number. For example, 3! = 3 \times 2 \times 1 = 6.

It can be expressed in product notation as \prod_{n=1}^{x} n, or in the form of a recurrence relation as n! = n \left( n - 1 \right)!.

0! is equal to one because it is the empty product.

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