Factory rhymes with:
olfactory, unsatisfactory, olfactory, refractory, unsatisfactory, contradictory, directory, introductory, olfactory, perfunctory, rectory, refractory, trajectory, unsatisfactory, valedictory, victory
Factory sounds like:
factor, faster, feaster, fechter, feister, fester, fichter, fiechter, fighter, fisheater, fister, fixture, foister, foster