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Factorial is defined as

$n! = n(n-1)(n-2)\cdots 1$

But why mathematicians named this thing as FACTORIAL?

Has it got something to do with factors?

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Interesting... Cajori discusses the various notations adopted over the years, but never a mention of why it was called the "factorial". Maybe this article: dx.doi.org/10.1007/BF00389433 has the answers. –  J. M. Aug 27 '10 at 10:14
I was once told that an alternative name for the factorial ! was "shriek" which makes EVEN LESS SENSE! –  Seamus Aug 27 '10 at 12:00
Seamus: It would probably interest you to know that it had been suggested at some point that n! be read as "n-admiration" (per Cajori). –  J. M. Aug 27 '10 at 12:14
this ought to be cw. –  Tom Stephens Aug 27 '10 at 15:01
I've heard of "shriek" as a name for the exclamation point symbol "!" in general, not just for its meaning of "factorial"; an emphatic word for an emphatic symbol. This seems to come from the computer science world, where it's now been superseded by "bang". See catb.org/jargon/html/B/bang.html, where the hard-to-pronounce "excl" is also cited. –  Nate Eldredge Aug 27 '10 at 16:39

2 Answers 2

up vote 7 down vote accepted

Well, all positive integers smaller or equal to n are factors of n!

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But that's true of other numbers (both smaller and larger) that aren't the factorial. –  Ben Alpert Apr 28 '11 at 20:54

Below is the etymology, from Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics (F). Perhaps a native French speaker can lend further insight.

FACTORIAL. The earlier term faculty was introduced around 1798 by Christian Kramp (1760-1826).

Factorial was coined (in French as factorielle) by Louis François Antoine Arbogast (1759-1803).

Kramp withdrew his term in favor of Arbogast's term. In the Preface, pp. xi-xii, of his "Éléments d'arithmétique universelle," Hansen, Cologne (1808), Kramp remarks:

...je leur avais donné le nom de facultés. Arbogast lui avait substitué la nomination plus nette et plus française de factorielles; j'ai reconnu l'avantage de cette nouvelle dénomination; et en adoptant son idée, je me suis félicité de pouvoir rendre hommage à la mémoire de mon ami. [...I've named them facultes. Arbogast has proposed the denomination factorial, clearer and more French. I've recognised the advantage of this new term, and adopting its philosophy I congratulate myself of paying homage to the memory of my friend.]

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Interesting! "faculty" is still used in German (as "Fakultät"). –  Jens Nov 9 '10 at 7:23
In Norway we call it "fakultet". –  please delete me May 10 '11 at 15:50

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