factor (n.) Look up factor at Dictionary.com
early 15c., "agent, deputy," from Middle French facteur "agent, representative," from Latin factor "doer or maker," agent noun from past participle stem of facere "to do" (see factitious). Sense of "circumstance producing a result" is from 1816.
factor (v.) Look up factor at Dictionary.com
1610s, "act as an agent," from factor (n.). The use in mathematics is attested from 1837. Related: Factored; factoring.