[fak-tawr-ee-uh
l, -tohr-] 
| 1. | Mathematics. the product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) = 4 · 3 · 2 · 1 = 24. Symbol: n!, where n is the given integer. |
| 2. | Mathematics. of or pertaining to factors or factorials. |
| 3. | of or pertaining to a factor or a factory. |
| fac·to·ri·al (fāk-tôr'ē-əl, -tōr'-) n. The product of all the positive integers from 1 to a given number: 4 factorial, usually written 4!, is equal to 24 (1 × 2 × 3 × 4 = 24). adj. Of or relating to a factor or factorial. |
| factorial (fāk-tôr'ē-əl) Pronunciation Key
The product of all of the positive integers from 1 to a given positive integer. It is written as the given integer followed by an exclamation point. For example, the factorial of 4 (written 4!) is 1 × 2 × 3 × 4, or 24. |
factorial mathematics
The mathematical function that takes a natural number, N, and returns the product of N and all smaller positive integers. This is written
N! = N * (N-1) * (N-2) * ... * 1.
The factorial of zero is one because it is an empty product.
Factorial can be defined recursively as
0! = 1 N! = N * (N-1)! , N > 0
The gamma function is the equivalent for real numbers.
(2005-01-07)