As nouns the difference between factory and school
is that
factory is (obsolete) a trading establishment, especially set up by merchants working in a foreign country while
school is a group of fish or a group of marine mammals such as porpoises, dolphins, or whales or
school can be (us|canada) an institution dedicated to teaching and learning; an educational institution.
As a verb school is
(of fish) to form into, or travel in a school or
school can be to educate, teach, or train (often, but not necessarily, in a school).