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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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Factorial -

Tag(s) : Arithmetics, Mathematics

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Factorial

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

Answers to Questions

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 numbershref. 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. $$ n!\sim\sqrt{2\pi n}\left(\frac{n}{e}\right)^n $$

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