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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: [[[>40 It's interesting that the formula to approximate the factorial involves both $e$ and $\pi$ ]]] * Stirling's formula gives an approximation of the factorial: ** $n!~{\approx}~n^ne^{-n}\sqrt{2\pi{n}}$ *** ... where $e$ is Euler's Number. * 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. ** See Modulo Arithmetic ---- Enrichment tasks: * 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. ---- * http://en.wikipedia.org/wiki/Factorial * http://www.google.com/search?q=Factorial