## Most recent change of Factorial

Edit made on March 16, 2010 by GuestEditor at 13:05:13

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HEADERS_END

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 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:

** EQN:n!{\approx}n^ne^{-n}\sqrt{2\pi{n}}

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

** EQN:n!=\int_0^\infty{e^{-x}}x^n.dx

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

See the Gamma Function

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

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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.

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* http://en.wikipedia.org/wiki/Factorial

* http://www.google.com/search?q=Factorial