[fak-tawr-ee-uhl, -tohr-]
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.
Mathematics. of or pertaining to factors or factorials.
of or pertaining to a factor or a factory.

1810–20; factor + -ial

factorially, adverb
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Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
factorial (fækˈtɔːrɪəl)
1.  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
2.  of or involving factorials or factors

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

1816 (n.), 1837 (adj.), from factor + -al (2).
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Science Dictionary
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.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Computing Dictionary

factorial definition

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.
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Example sentences
It is probably a multi-factorial process of intrinsic aging and extrinsic aging.
The list of factorial and binomial topics contains a large number of related links.
If time is relative then measuring distance covered with time as a factorial to calculate speed or acceleration is misleading.
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