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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.

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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Definitions of factor from WordNet
1
factor (n.)
anything that contributes causally to a result;
a number of factors determined the outcome
factor (n.)
an abstract part of something;
a key factor in her success
factor (n.)
one of two or more integers that can be exactly divided into another integer;
what are the 4 factors of 6?
Synonyms: divisor
factor (n.)
a businessman who buys or sells for another in exchange for a commission;
Synonyms: agent / broker
factor (n.)
any of the numbers (or symbols) that form a product when multiplied together;
factor (n.)
an independent variable in statistics;
factor (n.)
(genetics) a segment of DNA that is involved in producing a polypeptide chain; it can include regions preceding and following the coding DNA as well as introns between the exons; it is considered a unit of heredity;
genes were formerly called factors
Synonyms: gene / cistron
2
factor (v.)
resolve into factors;
a quantum computer can factor the number 15
Synonyms: factor in / factor out
factor (v.)
be a contributing factor;
make things factor into a company's profitability
factor (v.)
consider as relevant when making a decision;
You must factor in the recent developments
Synonyms: factor in / factor out
From wordnet.princeton.edu