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Probably from factor + y, although in noun sense 1 (“a place where manufacturing takes place”) apparently influenced strongly by association with Classical Latin fact-, the past participial stem of faciō (“to make”); compare manufactory and Latin factōrium (“an oil press”). In noun sense 8 (“a trading establishment”), originally after Portuguese feitoria. In noun sense 9 (“an invoice or inventory”), probably after obsolete Dutch facture (“bill”); see facture. Compare Dutch factorij, Middle French factorie, Spanish factoría.
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