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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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    I like saying $n!$ like "enn!!!!!!!!" in a really high, excited voice :)2014-02-07

2 Answers 2

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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.2011-04-28
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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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    Apparently, in Swedish too!2016-08-20