early 15c., "commercial agent, deputy, one who buys or sells for another," from Middle 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" (see factitious). In commerce, especially "a commission merchant." Mathematical sense is from 1670s. Sense of "circumstance producing a result" is attested by 1816, from the mathematical sense.

1610s, "act as an agent, manage," from factor, n.. The use in mathematics is attested from 1837. Related: Factored; factoring.