'undividability' originates from English, formed by the negative prefix 'un-' + the noun 'dividability' (ultimately from Latin 'dividere'), where the Latin root 'dividere' meant 'to divide'.

'dividere' changed into Old French 'diviser' and Middle English 'divide', producing English derivatives such as 'dividability'; the modern formation 'undividability' was created in English by adding 'un-' to that noun.

Initially the Latin root meant 'to divide', but over time the derived English noun 'undividability' came to mean 'the state or quality of not being divisible'.