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# factorial

## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• n. The product of all the positive integers from 1 to a given number: 4 factorial, usually written 4!, is equal to 24 (1 × 2 × 3 × 4 = 24).
• adj. Of or relating to a factor or factorial.

• n. The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 * 2 * 3 * 4 * 5 = 120.
• adj. Of or pertaining to a factor or factorial.
• adj. Of or pertaining to a factor.
• adj. Of or pertaining to a factory.

### from the GNU version of the Collaborative International Dictionary of English

• adj. Of or pertaining to a factory.
• n. 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.
• n. The product of the consecutive whole numbers from unity up to any given number.

### from The Century Dictionary and Cyclopedia

• Pertaining to a factor or factory; constituting a factory.
• In mathematics, of or pertaining to a factor or factorials. See II.
• n. In mathematics, a continued product of the form Fx, F(x+1), F(x+2), F(x+3), … F(x+n), in which every factor after the first is derived from the preceding by increasing the variable by unity.