# factorial

factorial
/fak tawr"ee euhl, -tohr"-/, n.
1. Math. the product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) = 4 · 3 · 2 · 1 = 24. Symbol: n!, where n is the given integer.
2. Math. of or pertaining to factors or factorials.
3. of or pertaining to a factor or a factory.
[1810-20; FACTOR + -IAL]

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For any whole number, the product of all the counting numbers up to and including itself.

It is indicated with an exclamation point: 4! (read "four factorial") is 1 × 2 × 3 × 4 = 24. In order for certain formulas involving permutations and combinations to work, 0! is defined to be 1. Factorials are particularly useful in calculating the number of ways an event can occur, for example, the number of possible orders of finish in a race.

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in mathematics, the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point. Thus, factorial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is defined as equal to 1.

Factorials are commonly encountered in the evaluation of permutations and combinations and in the coefficients of terms of binomial expansions (see binomial theorem). Factorials have been generalized to include nonintegral values (see gamma function).

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Universalium. 2010.

### Look at other dictionaries:

• factorial — FACTORIÁL, factoriale, adj. (mat.; în sintagma) Produs factorial (şi substantivat, n.) = produs obţinut prin înmulţirea numerelor întregi şi succesive începând de la 1 şi mergând până la numărul respectiv. [pr.: ri al] – Din fr. factorielle.… …   Dicționar Român

• 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 Collaborative International Dictionary of English

• factorial — (De factor). f. Mat. Producto que resulta de multiplicar un número entero positivo dado por todos los enteros inferiores a él hasta el uno. (Símb. !). El factorial de 4 es 4! = 4 x 3 x 2 x 1 = 24. ☛ V. análisis factorial …   Diccionario de la lengua española

• factorial — Mathematics ► NOUN ▪ the product of an integer and all the integers below it, e.g. 4 x 3 x 2 x 1 (factorial 4, denoted by 4! and equal to 24). ► ADJECTIVE ▪ relating to a factor or factorial. DERIVATIVES factorially adverb …   English terms dictionary

• factorial — adjetivo 1. Área: matemáticas Del factor o de los factores: Haz la descomposición factorial de 125. sustantivo femenino 1. Área: matemáticas Producto de todos los términos de una progresión aritmética …   Diccionario Salamanca de la Lengua Española

• factorial — [fak tôr′ē əl] adj. 1. of a factor 2. Math. of factors or factorials n. Math. the product of a given series of consecutive whole numbers beginning with 1 and ending with the specified number [the factorial of 5 (5!) is 1 × 2 × 3 × 4 × 5, or 120] …   English World dictionary

• Factorial — Fac*to ri*al, a. 1. Of or pertaining to a factory. Buchanan. [1913 Webster] 2. (Math.) Related to factorials. [1913 Webster] …   The Collaborative International Dictionary of English

• Factorial —   [engl.], Fakultät …   Universal-Lexikon

• factorial — 1816 (n.), 1837 (adj.), from FACTOR (Cf. factor) + AL (Cf. al) (2) …   Etymology dictionary

• factorial — |àt| adj. 2 g. 1. Referente a fatores. 2. Constituído por fatores.   ♦ [Portugal] Grafia de fatorial antes do Acordo Ortográfico de 1990.   ♦ Grafia no Brasil: fatorial …   Dicionário da Língua Portuguesa

• Factorial — n n! 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 …   Wikipedia