'factorability' originates from Latin via the noun 'factor' (from Latin 'facere'), where the root 'fac-' meant 'to do, to make', combined with the adjectival suffix '-able' (from Latin '-abilis') and the nominalizing suffix '-ity' (from Latin '-itas'), producing the sense 'capability of being factored'.

'factorability' developed from the Middle English noun 'factor' (from Latin 'factor', meaning 'maker' or 'doer'), which formed the adjective 'factorable' (able to be factored) and was later nominalized with '-ity' to create 'factorability'.

Initially related to 'maker' or 'doer' through 'factor', the term's modern formation and usage shifted to mean 'the property of being capable of being factored' (especially in mathematics).