The factorial of a number $n,$ written $n!,$ is the product of $n$ along with all the natural numbers smaller than $n$ (not including zero !!!).

Therefore, $n!=n \times(n-1)\times(n-2)\ldots3\times2\times1$

For example, 5! = 5 x 4 x 3 x 2 x 1 = 120

Here are some facts about the factorial:

It's interesting that the formula to approximate the factorial involves both $e$ and $\pi$

There is also a version of the factorial that is defined for (some) non-integers:

See the Gamma Function.

Wilson's Theorem says that $(n-1)!\equiv-1\quad(mod~{n})$ if and only if $n$ is a prime number.

Enrichment tasks:

(none)	(none)			Banach-TarskiParadox BinomialCoefficient BinomialTheorem
↓	↓		↓	↓
ZeroFactorial			BirthdayProblem MathematicsTaxonomy PascalsTriangle Permutation
			↓
		⇌	You are here Factorial
			↓
			EulersNumber Function Integer ModuloArithmetic NaturalNumber PrimeNumber
↓	↓		↓	↓
(none)	(none)			CoDomainOfAFunction CompositeNumber CountingNumber Divisor DomainOfAFunction EuclideanAlgorithm Euler FermatsLittleTheorem ImageOfAFunction Logarithm NaturalLogarithm Polynomial PrimePair RangeOfAFunction RealNumber WholeNumber

Local neighbourhood - D3

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Factorial