From Latin 'factor' (doer, maker) — entered English as a commercial agent before acquiring mathematical and general senses.
Definition
An element or circumstance that contributes to a result; also, a person who acts on behalf of another, or a number that divides into another exactly.
The Full Story
Latin15th centurywell-attested
From Latin 'factor' (doer, maker, performer, one who acts), an agent noun from 'facere' (to do, to make, to perform), from PIE *dʰeh₁- (to put, to place, to do, to make). The word entered Middle English via Old French 'facteur' in the fifteenth century, initially meaning a commercial agent or deputy — someone who 'does' business on another's behalf, a sense preserved in the Scottish term 'factor' for an estate manager. The mathematical sense (a number that produces another number when multiplied) developed in the seventeenth century, abstracting
Did you know?
In Scotland, a 'factor' still means a land agent or estate manager — the original English sense from the fifteenth century. Meanwhile, the same Latin root 'facere' gave us 'fact' (a thing done), 'factory' (a place of making), and even '-fy' in words like 'magnify' and 'satisfy.'
to do), 'fashion' (a manner of doing), 'feasible' (doable), 'feat' (a deed), 'feature' (a made thing, a form), 'affair' (something to do — via French 'à faire'), 'benefit' (a good deed), 'defeat' (to undo), 'defect' (something undone, a flaw), 'effect' (something done out, a result), 'infect' (to put into, to taint), 'perfect' (thoroughly done), 'sacrifice' (to make sacred), 'satisfy' (to do enough), 'sufficient' (doing under,
enough), and 'magnificent' (making great). Through Greek 'tithenai' (to place) came 'thesis,' 'theme,' 'apothecary.' Through Germanic *dōn came Old English 'dōn,' giving modern 'do' and 'deed.' Factor thus connects directly to the most basic English verb of action. Key roots: facere (Latin: "to do, to make, from PIE *dʰeh₁- (to put, place, make)").