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