factorial

== English == === Etymology === From factor +‎ -ial. === Pronunciation === IPA(key): /fækˈtɔːɹi.əl/ Rhymes: -ɔːɹiəl === Noun === factorial (plural factorials) (mathematics, combinatorics) 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. ==== Usage notes ==== "n!" is read as "factorial of n" or "n factorial." ==== Hyponyms ==== double factorial falling factorial rising factorial ==== Related terms ==== ==== Translations ==== === Adjective === factorial (comparative more factorial, superlative most factorial) (mathematics) Of or pertaining to a factor or factorial. Of or pertaining to a factor, a kind of business agent. (dated) Of or pertaining to a factory. === Derived terms === === See also === primorial === References === factorial on Wikipedia.Wikipedia === Further reading === “factorial”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC. William Dwight Whitney, Benjamin E[li] Smith, editors (1911), “factorial”, in The Century Dictionary […], New York, N.Y.: The Century Co., →OCLC. == Portuguese == === Noun === factorial m (plural factoriais) pre-reform spelling (used until 1943 in Brazil and 1990 in Portugal) of fatorial; still used where the agreement hasn’t come into effect and may occur as a sporadic misspelling === Adjective === factorial m or f (plural factoriais) pre-reform spelling (used until 1943 in Brazil and 1990 in Portugal) of fatorial; still used where the agreement hasn’t come into effect and may occur as a sporadic misspelling === Further reading === “factorial”, in Dicionário Priberam da Língua Portuguesa (in Portuguese), Lisbon: Priberam, 2008–2026 == Romanian == === Etymology === Borrowed from French factorielle. === Adjective === factorial m or n (feminine singular factorială, masculine plural factoriali, feminine/neuter plural factoriale) factorial ==== Declension ==== == Spanish == === Etymology === From French factorielle. Equivalent to factor +‎ -al. === Pronunciation === IPA(key): /faɡtoˈɾjal/ [faɣ̞.t̪oˈɾjal] Rhymes: -al Syllabification: fac‧to‧rial === Adjective === factorial m or f (masculine and feminine plural factoriales) factorial ==== Derived terms ==== === Noun === factorial m (plural factoriales) (mathematics) factorial === Further reading === “factorial”, in Diccionario de la lengua española [Dictionary of the Spanish Language] (in Spanish), online version 23.8.1, Royal Spanish Academy [Spanish: Real Academia Española], 15 December 2025