• (RP) IPA: /ˈfæktə/
• (GA) IPA: /ˈfæktɚ/

factor (plural factors)

1. (obsolete) A doer, maker; a person who does things for another person or organization.

   The factor of the trading post bought the furs.

2. (now rare) An agent or representative.

   My factor sends me word, a merchant's fled / That owes me for a hundred tun of wine.

   • 1603, Michel de Montaigne, chapter 21, in John Florio, transl., The Essayes, […], book II, printed at London: By Val[entine] Simmes for Edward Blount […], OCLC 946730821 ↗:

     And let such as will number the Kings of Castile and Portugall amongst the warlike and magnanimous conquerors, seeke for some other adherent then my selfe, forsomuch as twelve hundred leagues from their idle residence they have made themselves masters of both Indias, onely by the conduct and direction of their factors, of whom it would be knowne whether they durst but goe and enjoy them in person.

   • 1644, John Milton, Aeropagitica:

     What does he therefore, but resolvs to give over toyling, and to find himself out som factor, to whose care and credit he may commit the whole managing of his religious affairs; som Divine of note and estimation that must be.

   1985 Haynes Owners Workshop Manual, BMW

   Motor factors — Good factors will stock all of the more important components which wear out relatively quickly.

3. (legal)
   1. A commission agent.
   2. A person or business organization that provides money for another's new business venture; one who finances another's business.
   3. A business organization that lends money on accounts receivable or buys and collects accounts receivable.
4. One of the elements, circumstances, or influences which contribute to produce a result.

   The greatest factor in the decision was the need for public transportation.

   The economy was a factor in this year's budget figures.

   • the material and dynamical factors of nutrition

5. (mathematics) Any of various objects multiplied together to form some whole.

   3 is a factor of 12, as are 2, 4 and 6.

   The factors of the Klein four-group are both cyclic of order 2.

   • 1956, Arthur C. Clarke, The City and the Stars, p.38:

     The first thousand primes […] marched in order before him […] the complete sequence of all those numbers that possessed no factors except themselves and unity.

6. (root cause analysis) Influence; a phenomenon that affects the nature, the magnitude, and/or the timing of a consequence.

   The launch temperature was a factor of the Challenger disaster.

7. (economics) A resource used in the production of goods or services, a factor of production.
8. (Scotland) A steward or bailiff of an estate.

• fact
• faction
• factory
• fashion

• Portuguese: fator, fazedor
• Russian: комиссионе́р

• German: Faktor
• Italian: fattore
• Portuguese: factor
• Russian: фа́ктор
• Spanish: factor

• French: facteur
• German: Faktor
• Italian: fattore
• Portuguese: fator
• Russian: множитель
• Spanish: factor

• French: facteur
• German: Faktor
• Italian: fattore, fattore
• Portuguese: fator
• Russian: причина
• Spanish: factor

factor (factors, present participle factoring; past and past participle factored)

1. (transitive) To find all the factors of (a number or other mathematical object) (the objects that divide it evenly).
2. (of a number or other mathematical object, intransitive) To be a product of other objects.
3. (commercial, transitive) To sell a debt or debts to an agent (the factor) to collect.

• French: factoriser
• Italian: fattorizzare
• Spanish: factorizar

1. Surname