# factorial

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## factorial

Maths
the product of all the positive integers from one up to and including a given integer. Factorial zero is assigned the value of one: factorial four is 1 × 2 × 3 × 4. Symbol: n!, where n is the given integer
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Factorial

The factorial of a given natural number n is the product of all the natural numbers less than or equal to n. The factorial of n is denoted usually by n! Thus,

n! = 1 × 2 × ... × n

For large n an approximate expression for n! is given by Stirling’s formula. The number of permutations of n things taken all at a time is the factorial of n.

## factorial

[fak′tȯr·ē·əl]
(mathematics)
The product of all positive integers less than or equal to n; written n !; by convention 0! = 1.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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.

## factorial

The number of sequences that can exist with a set of items, derived by multiplying the number of items by the next lowest number until 1 is reached. For example, three items have six sequences (3x2x1=6): 123, 132, 231, 213, 312 and 321. See factor and IFP.
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