Etymology
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factor (n.)

early 15c., "commercial agent, deputy, one who buys or sells for another," from French facteur "agent, representative" (Old French factor, faitor "doer, author, creator"), from Latin factor "doer, maker, performer," in Medieval Latin, "agent," agent noun from past participle stem of facere "to do" (from PIE root *dhe- "to set, put"). In commerce, especially "a commission merchant." Mathematical sense ("The Quantities given to be multiplied one by the other are called Factors") is from 1670s. Sense of "circumstance producing a result" is attested by 1816, from the mathematical sense.

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factor (v.)
1610s, "act as an agent, manage," from factor (n.). The use in mathematics is attested from 1837. Related: Factored; factoring.
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factorial (n.)
1816, in mathematics, from factor + -al (2). As an adjective from 1837 in mathematics; from 1881 as "pertaining to a factor."
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multifactorial (adj.)

also multi-factorial, "involving or dependent on a number of factors," 1920, from multi- "many" + factor (n.) + -ial.

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Rh factor 
1942, from the first letters of rhesus; so called because the blood group, and its effects, were discovered in the blood of rhesus monkeys (1941).
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*dhe- 

*dhē-, Proto-Indo-European root meaning "to set, put."

It forms all or part of: abdomen; abscond; affair; affect (v.1) "make a mental impression on;" affect (v.2) "make a pretense of;" affection; amplify; anathema; antithesis; apothecary; artifact; artifice; beatific; benefice; beneficence; beneficial; benefit; bibliothec; bodega; boutique; certify; chafe; chauffeur; comfit; condiment; confection; confetti; counterfeit; deed; deem; deface; defeasance; defeat; defect; deficient; difficulty; dignify; discomfit; do (v.); doom; -dom; duma; edifice; edify; efface; effect; efficacious; efficient; epithet; facade; face; facet; facial; -facient; facile; facilitate; facsimile; fact; faction (n.1) "political party;" -faction; factitious; factitive; factor; factory; factotum; faculty; fashion; feasible; feat; feature; feckless; fetish; -fic; fordo; forfeit; -fy; gratify; hacienda; hypothecate; hypothesis; incondite; indeed; infect; justify; malefactor; malfeasance; manufacture; metathesis; misfeasance; modify; mollify; multifarious; notify; nullify; office; officinal; omnifarious; orifice; parenthesis; perfect; petrify; pluperfect; pontifex; prefect; prima facie; proficient; profit; prosthesis; prothesis; purdah; putrefy; qualify; rarefy; recondite; rectify; refectory; sacrifice; salmagundi; samadhi; satisfy; sconce; suffice; sufficient; surface; surfeit; synthesis; tay; ticking (n.); theco-; thematic; theme; thesis; verify.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dadhati "puts, places;" Avestan dadaiti "he puts;" Old Persian ada "he made;" Hittite dai- "to place;" Greek tithenai "to put, set, place;" Latin facere "to make, do; perform; bring about;" Lithuanian dėti "to put;" Polish dziać się "to be happening;" Russian delat' "to do;" Old High German tuon, German tun, Old English don "to do."

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factory (n.)

1550s, "estate manager's office," from French factorie (15c.), from Late Latin factorium "office for agents ('factors')," also "oil press, mill," from Latin factor "doer, maker," agent noun from past-participle stem of facere "to do" (from PIE root *dhe- "to set, put"). From 1580s as "establishment of merchants and factors in a foreign place." Sense of "building for making goods" is first attested 1610s. Factory farm is attested from 1890.

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parameter (n.)

1650s in geometry, in reference to conic sections, from Modern Latin parameter (1630s), from Greek para- "beside, subsidiary" (see para- (1)) + metron "measure" (from PIE root *me- (2) "to measure").

A geometry term until late 1920s when it began to be extended to "measurable factor which helps to define a particular system," hence the common meaning (influenced by perimeter) of "boundary, limit, characteristic factor," common from 1950s. Related: Parametric; parametrical.

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particular (n.)

late 14c., particuler, "a part or section of a whole, an individual circumstance, feature, or factor; an organ or part of the body," from particular (adj.). Meaning "a single instance or matter" is from 1530s; particulars "small details of statement" is from c. 1600.

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biotic (adj.)

"pertaining to life," 1847, also biotical (1847), from Latin bioticus, from Greek biotikos "pertaining to life," from bios "life," from PIE root *gwei- "to live." Biotic factor was in use by 1907. Related: Biotical. Biotics "science of vital functions and manifestations; powers and qualities peculiar to living organisms" (T. Sterry Hunt) is from 1882.

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