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 $\pi$

• Stirling's formula gives an approximation of the factorial:
• $n!~{\approx}~n^ne^{-n}\sqrt{2\pi{n}}$
• There is also a version of the factorial that is defined for (some) non-integers:
• $n!=\int_0^\infty{e^{-x}}x^n.dx$
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.

• How many zeros are there at the end of 2009!
• What is Zero Factorial?
• Use Wilson's theorem to test whether 6 and 7 are prime numbers.

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ZeroFactorial BirthdayProblem
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Factorial
EulersNumber
Function
Integer
ModuloArithmetic
NaturalNumber
(none) (none) CoDomainOfAFunction
CompositeNumber
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DomainOfAFunction
EuclideanAlgorithm
Euler
FermatsLittleTheorem
ImageOfAFunction
Logarithm
NaturalLogarithm
Polynomial
PrimePair
RangeOfAFunction
RealNumber
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