factorial

English

Etymology

factor +‎ -ial

Pronunciation

• IPA^(key): /fækˈtɔːɹi.əl/

  • Audio (UK):

    (file)

Noun

factorial (plural factorials)

1. (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

• fact
• faction
• factor
• factorial prime
• factory
• fashion

 

Translations

mathematical operation or its result

• Bulgarian: факториа́л m (faktoriál)
• Chinese:

  Mandarin: 階乘／阶乘 (zh) (jiēchéng)

• Czech: faktoriál m
• Danish: fakultet
• Dutch: faculteit (nl)
• Estonian: faktoriaal
• Finnish: kertoma (fi)
• French: factorielle (fr) f
• German: Fakultät (de) f
• Greek: παραγοντικό (el) m (paragontikó)
• Hebrew: עֲצֶרֶת (he) f ('atzerét)
• Hungarian: faktoriális (hu)
• Icelandic: aðfeldi (is) n, (a factorial number) hrópmerkt tala f, (factorial of five) fimm hrópmerkt, (factorial of five) fimm aðfaldað
• Irish: iolrán m
• (deprecated template usage) {{trans-mid}}
• Italian: fattoriale (it) m
• Japanese: 階乗 (ja) (kaijō)
• Korean: 계승 (ko) (gyeseung)
• Kyrgyz: факториал (ky) (faktorial)
• Norwegian:

  Bokmål: factorial n

• Polish: silnia (pl) f, (dated) faktoriał m
• Portuguese: fatorial (pt) m
• Russian: факториа́л (ru) (faktoriál)
• Spanish: factorial (es) m
• Swedish: fakultet (sv) c
• Tagalog: buuin
• Turkish: faktöriyel (tr)
• Vietnamese: giai thừa

Adjective

factorial (comparative more factorial, superlative most factorial)

1. (mathematics) Of or pertaining to a factor or factorial.
2. Of or pertaining to a factor, a kind of business agent.
   • 2004, The Digest: Annotated British, Commonwealth, and European Cases

     The latter sold the goods to a customer who was cashier to certain creditors of the agents without disclosing the factorial capacity in which they acted.

3. (dated) Of or pertaining to a factory.

See also

• primorial

References

• factorial on Wikipedia.Wikipedia

Further reading

• “factorial”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• “factorial”, in The Century Dictionary […], New York, N.Y.: The Century Co., 1911, →OCLC.

---

Portuguese

Noun

factorial m (plural factoriais)

1. Template:pt-superseded-silent-letter-1990

Adjective

factorial m or f (plural factoriais)

1. Template:pt-superseded-silent-letter-1990

---

Romanian

Etymology

From French factorielle.

Adjective

factorial m or n (feminine singular factorială, masculine plural factoriali, feminine and neuter plural factoriale)

1. factorial

Declension

Declension of factorial

		singular			plural
		masculine	neuter	feminine	masculine	neuter	feminine
nominative/ accusative	indefinite	factorial		factorială	factoriali	factoriale
	definite	factorialul		factoriala	factorialii	factorialele
genitive/ dative	indefinite	factorial		factoriale	factoriali	factoriale
	definite	factorialului		factorialei	factorialilor	factorialelor

---

Spanish

Noun

factorial m (plural factoriales)

1. (mathematics) factorial

Further reading

• “factorial”, in Diccionario de la lengua española (in Spanish), online version 23.7, Royal Spanish Academy, 2023 November 28