'factorize' originates from Modern English, specifically formed from the noun 'factor' plus the verbalizing suffix '-ize', where 'factor' ultimately comes from Latin 'factor' meaning 'maker, doer' and '-ize' comes via Greek '-izein'/'-ismos' (through Latin and French) meaning 'to make or to render'.

'factorize' was formed in Modern English by combining the Latin-derived element 'factor' with the productive suffix '-ize' (from Greek via Latin/French), producing the verb 'factorize' used in mathematical contexts from the 19th century onward.

Initially it meant 'to make or render into factors' and over time it has come to be used specifically in mathematics to mean 'to express as a product of factors' (including prime factorization for integers).