factoryyoudaoicibaDictYouDict[factory 词源字典]
factory: [16] Latin factor, a derivative of facere ‘make’, meant ‘maker, doer’ (it was introduced into English in the 15th century as ‘agent’, but was not adopted as a mathematical term until the mid 17th century). Among its post-classical derivatives were late Latin factōrium ‘oil-press’ and medieval Latin factōria ‘establishment for factors or agents’.

It appears that the latter must have been the original source of the word factory in English, which at first meant ‘factorship, agency’. However, this does not fit in at all with its main modern sense ‘place where things are made’, first recorded in the early 17th century, which presumably must go back in some way to Latin factōrium.
=> fact[factory etymology, factory origin, 英语词源]
factory (n.)youdaoicibaDictYouDict
1550s, "estate manager's office," from Middle French factorie (15c.), from Late Latin factorium "office for agents ('factors')," also "oil press, mill," from Latin factor "doer, maker" (see factor (n.)). From 1580s as "establishment of merchants and factors in a foreign place." Sense of "building for making goods" is first attested 1610s. Factory farm attested from 1890.