Factorizable

Part of speech: adjective

Definitions

1. Able to be expressed as a product of smaller whole numbers or algebraic terms that multiply together to give the original value
2. Describing a number or expression that can be split into factors which, when multiplied, produce it exactly
3. Capable of being resolved into component factors, as a number or polynomial can be broken down into simpler multiplicative parts

Etymology: "Factorizable" is a plain modern formation, built in English from "factorize" plus the suffix "-able," meaning "capable of being done." "Factorize" is itself a derivation from "factor," a word that came into English from Latin "factor," "a doer or maker," from "facere," "to do or make." The sense of "factor" as a mathematical term, a number that divides another exactly, comes from the idea of a number that "makes" a product when multiplied with another. The verb "factorize" follows the pattern of words ending in "-ize," which English took from Greek-derived forms through Latin and French. Adding "-able" gives the sense "able to be broken down into factors." So a number like 15 is factorizable into 3 and 5, while a prime number is not.