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Factorial

Tool for computing factorials. Factorial n! is the product of all integers numbers (not zero) inferior or equal to n.

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Tag(s) : Arithmetics, Mathematics

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# Factorial

## Gamma Calculator Γ(N)

Tool for computing factorials. Factorial n! is the product of all integers numbers (not zero) inferior or equal to n.

### How to calculate a factorial?

Factorial of a number $$n$$ is calculated with a simple multiplication: it is the product of the positive integers numbers (not null) less or equal to $$n$$.

The usual notation to indicate a factorial is the exclamation mark positioned after the number. The factorial of $$n$$ is noted $$n!$$.

$$n!=\prod_{k=1}^n k$$

Example: $$4! = 1 \times 2 \times 3 \times 4 = 24$$

Note that the factorial of zero is equal to one : $$0! = 1$$

Example: Here are the values of the first factorials $$0! = 1 \\ 1! = 1 \\ 2! = 2 \\ 3! = 6 \\ 4! = 24 \\ 5! = 120 \\ 6! = 720 \\ 7! = 5040 \\ 8! = 40320 \\ 9! = 362880 \\ 10! = 3628800$$

### What is the Gamma Function?

Euler-Gamma is an extension of the factorial function over the Complex numbers. dCode offers calculation over the Reals. $$\forall\,n \in \mathbb{N}, \; \Gamma(n+1)=n!$$

### How to calculate a negative factorial?

Use the Gamma function.

### How to quickly compute a factorial value?

For large numbers, it is possible to estimate the value of $$n!$$ with a good precision using the Stirling formula. $$n!\sim\sqrt{2\pi n}\left(\frac{n}{e}\right)^n$$