Fac*to"ri*al, n. (Math.) (a) pl. A name given to the factors of a continued product when the former are derivable from one and the same function F(x) by successively imparting a constant increment or decrement h to the independent variable. Thus the product F(x).F(x + h).F(x + 2h) . . . F[x + (n-1)h] is called a factorial term, and its several factors take the name of factorials. Brande & C.
(b) The product of the consecutive whole numbers from unity up to any given number; thus, 5
factorial is the product of 5 times four times three times two times one, or 120.
[1913 Webster +PJC]
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