'factorise' originates from English formation using the noun 'factor' and the verb-forming suffix '-ize' (via Old French '-iser' from Greek '-izein'), where the Latin root 'facere' meant 'to make or do'.

'factorise' changed from the English formation combining 'factor' (from Latin 'factor') with the suffix '-ize' (borrowed through French as '-iser'), and eventually became the modern English verb 'factorise' (British spelling) / 'factorize' (US spelling).

Initially, formation around 'factor' carried the sense 'to make or regard as a factor'; over time it evolved into the specific modern meaning 'to express as factors or to break into factors' (especially in mathematics).