'factorizability' originates from English, formed from 'factor' (from Latin 'factor', from 'facere' meaning 'to do or make'), the verb-forming suffix '-ize' (from Greek via Latin and Old French, meaning 'to make or become'), and the nominalizing suffix '-ability' (from Latin '-abilitas', meaning 'the ability to be').

'factorizability' changed from the modern English verb 'factorize' (which itself was formed from 'factor', borrowed from Latin 'factor' via Old French) and the noun-forming suffix '-ability'; these elements combined in Modern English to produce 'factorizability'.

Initially 'factor' meant 'maker' or 'doer' in Latin; through derivation and combination with '-ize' and '-ability', the compound evolved to mean 'the capability of being factored', which is its current meaning.