The DICT Development Group

  Factorial \Fac*to"ri*al\, a.
     1. Of or pertaining to a factory. --Buchanan.
        [1913 Webster]
  
     2. (Math.) Related to factorials.
        [1913 Webster]

  Factorial \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]

  factorial
      adj 1: of or relating to factorials
      n 1: the product of all the integers up to and including a given
           integer; "1, 2, 6, 24, and 120 are factorials"

  factorial
  
      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.
  
     For example, the number of ways of shuffling 52 playing cards is
     52! or nearly 10^68.  52 Factorial
     http://czep.net/weblog/52cards.html)">(http://czep.net/weblog/52cards.html).
  
     (2012-11-23)