Factorial

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Therefore, n! = n x (n - 1) x (n - 2) ... 3 x 2 x 1

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

Here are some facts about the factorial:

• 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:
• $n!=\int_0^\infty{e^{-x}}x^n.dx$

• Wilson's Theorem says that $(n-1)!\equiv-1\quad(mod\quad{n})$ if and only if n is a prime number. For information about $\quad(mod\quad{n})$ see Modulo Arithmetic

Enrichment task

• 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