I was researching factors as factor intermediaries, and its etymology on Etymonline.
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" (from PIE root *dhe- "to set, put").
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.
- What "mathematical sense" "from 1670s" does Etymonline mean? 'Factor ' is too polysemous!
- A term in multiplication
- Divisor, an integer which evenly divides a number without leaving a remainder
- Factorization, the decomposition of an object into a product of other objects
- Integer factorization, the process of breaking down a composite number into smaller non-trivial divisors
- A coefficient, a multiplicative factor in an expression, usually a number
- The act of forming a factor group or quotient ring in abstract algebra
- A von Neumann algebra, with a trivial center
- Factor (graph theory), a spanning sub graph
- Any finite contiguous sub sequence of a word in group theory
- Why did mathematicians in 1670s borrowed "factor"? Commission merchants in 1670s probably had to multiply and divide, but they also had to add and subtract too.
It’s an extension of the sense ‘maker’ of Latin factor: a factor of a number is in a sense one of its ‘makers’, one of its constituent parts. This is the earliest mathematical sense noted in the OED Third Edition, which has this 1658 citation from George Atwell, The faithfull surveyour discovering divers errours in land measuring, and showing how to measure all manner of ground, and to plot it, and to prove the shutting by the chain onely ...: