Etymology
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factitive (adj.)
"causative, expressive of making or causing," 1813, from Latin factus, past participle of facere "to make, do" (from PIE root *dhe- "to set, put") + -ive.
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factoid (n.)

1973, "published statement taken to be a fact because of its appearance in print," from fact + -oid, first explained, if not coined, by Norman Mailer.

Factoids ... that is, facts which have no existence before appearing in a magazine or newspaper, creations which are not so much lies as a product to manipulate emotion in the Silent Majority. [Mailer, "Marilyn," 1973]

By 1988 it was being used in the sense of "small, isolated bit of true factual information."

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factor (n.)

early 15c., "commercial agent, deputy, one who buys or sells for another," from French facteur "agent, representative" (Old French factor, faitor "doer, author, creator"), from Latin factor "doer, maker, performer," in Medieval Latin, "agent," agent noun from past participle stem of facere "to do" (from PIE root *dhe- "to set, put"). In commerce, especially "a commission merchant." Mathematical sense ("The Quantities given to be multiplied one by the other are called Factors") is from 1670s. Sense of "circumstance producing a result" is attested by 1816, from the mathematical sense.

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factor (v.)
1610s, "act as an agent, manage," from factor (n.). The use in mathematics is attested from 1837. Related: Factored; factoring.
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factorial (n.)
1816, in mathematics, from factor + -al (2). As an adjective from 1837 in mathematics; from 1881 as "pertaining to a factor."
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factory (n.)

1550s, "estate manager's office," from French factorie (15c.), from Late Latin factorium "office for agents ('factors')," also "oil press, mill," from Latin factor "doer, maker," agent noun from past-participle stem of facere "to do" (from PIE root *dhe- "to set, put"). From 1580s as "establishment of merchants and factors in a foreign place." Sense of "building for making goods" is first attested 1610s. Factory farm is attested from 1890.

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factotum (n.)
"one who does all kinds of work for another," 1560s, from Medieval Latin factotum "do everything," from fac, imperative of facere "to make, do" (from PIE root *dhe- "to set, put") + totum "all" (see total (adj.)).
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factual (adj.)
1834, formed from fact on model of actual. Related: Factually.
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faculties (n.)
"powers or properties of one's mind," also "physical functions," early 16c., plural of faculty.
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faculty (n.)
late 14c., "ability, opportunity, means, resources," from Old French faculte "skill, accomplishment, learning" (14c., Modern French faculté) and directly from Latin facultatem (nominative facultas) "power, ability, capability, opportunity; sufficient number, abundance, wealth," from *facli-tat-s, from facilis "easy to do," of persons, "pliant, courteous, yielding," from facere "to do" (from PIE root *dhe- "to set, put").

Academic sense "branch of knowledge" (late 14c.) was in Old French and probably was the earliest in English (it is attested in Anglo-Latin from late 12c.), on notion of "ability in knowledge" or "body of persons on whom are conferred specific professional powers." Originally each department was a faculty; the use in reference to the whole teaching staff of an entire college dates from 1767. Related: Facultative. The Latin words facultas and facilitas "were originally different forms of the same word; the latter, owing to its more obvious relationship to the adj., retained the primary sense of 'easiness', which the former had ceased to have before the classical period." [OED]
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