Online Etymology Dictionary

factitious (adj.): 1640s, "made by or resulting from art, artificial," from Latin facticius/factitius "artificial," from factus "elaborate, artistic," past participle adjective from facere "to make, do; perform; bring about; endure, suffer; behave; suit, be of service" (source of French faire, Spanish hacer), from PIE root *dhe- "to put, to set, to do" (source also of Sanskrit dadhati "puts, places;" Avestan dadaiti "he puts;" Old Persian ada "he made;" Hittite dai- "to place;" Greek tithenai "to put, set, place;" Lithuanian deti "to put;" Polish dziać się "to be happening;" Russian delat' "to do;" Old High German tuon, German tun, Old Saxon, Old English don "to do;" Old Frisian dua, Old Swedish duon, Gothic gadeths "a doing;" Old Norse dalidun "they did"). Related: Factitiously; factitiousness.
factitive (adj.): "causative, expressive of making or causing," 1813, from Latin factus, past participle of facere "to make, do" (see factitious) + -ive.
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."
factor (n.): early 15c., "commercial agent, deputy, one who buys or sells for another," from Middle 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" (see factitious). In commerce, especially "a commission merchant." Mathematical sense is from 1670s. Sense of "circumstance producing a result" is attested by 1816, from the mathematical sense.
factor (v.): 1610s, "act as an agent, manage," from factor (n.). The use in mathematics is attested from 1837. Related: Factored; factoring.
factorial (n.): 1816, in mathematics, from factor + -al (2). As an adjective from 1837 in mathematics; from 1881 as "pertaining to a factor."
factory (n.): 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.
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" (see factitious) + totum "all" (see total (adj.)).
factual (adj.): 1834, formed from fact on model of actual. Related: Factually.
faculties (n.): "powers or properties of one's mind," also "physical functions," early 16c., plural of faculty.
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 (see facile).

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]
fad (n.): 1834, "hobby, pet project" (adjective faddy is from 1824), of uncertain origin. Perhaps shortened from fiddle-faddle. Or perhaps from French fadaise "trifle, nonsense," which is ultimately from Latin fatuus "stupid." From 1881 as "fashion, craze," or as Century Dictionary has it, "trivial fancy adopted and pursued for a time with irrational zeal."
faddish (adj.): 1855, from fad + -ish. Related: Faddishness.
faddle (v.): "to make much of a child," 1680s. Related: Faddled; faddling.
fade (v.): early 14c., "lose brightness, grow pale," from Old French fader "become weak, wilt, wither," from fade (adj.) "pale, weak; insipid, tasteless" (12c.), probably from Vulgar Latin *fatidus, which is said to be a blending of Latin fatuus "silly, tasteless" and vapidus "flat, flavorless." Related: Faded; fading. Of sounds, by 1819. Transitive sense from 1590s; in cinematography from 1918.
Adieu! adieu! thy plaintive anthem fades
Past the near meadows, over the still stream,
Up the hill-side; and now 'tis buried deep
In the next valley-glades:
Was it a vision, or a waking dream?
Fled is that music:--Do I wake or sleep?

[Keats, "Ode to a Nightingale"]
fade (n.): early 14c., "loss of freshness or vigor," from fade (adj.), c. 1300, " lacking in brilliance; pale, discolored, dull," from Old French fade (see fade (v.)). As a type of tapering hairstyle from 1988 (fade-out style is in a 1985 "Ebony" article on men's haircuts).
fade-out (n.): 1918, from verbal phrase, from fade (v.) + out (adv.).
fader (n.): sound control device, 1931, agent noun from fade (v.).
fado (n.): popular music style of Portugal, 1902, from Latin fatum "fate, destiny" (see fate (n.)). Because the songs tell the fates of their subjects.
fadoodle (n.): "something worthless or foolish," 1660s.
faecal (adj.): see fecal.
faeces (n.): see feces.
faerie (n.): supernatural kingdom, "Elfland," c. 1300, from Old French fairie; see fairy.
faery: see faerie.
fag (v.1): "to droop, decline in strength, become weary" (intransitive), 1520s, of uncertain origin; OED is content with the "common view" that it is an alteration of flag (v.) in its sense of "droop, go limp." Transitive sense of "to make (someone or something) fatigued, tire by labor" is first attested 1826. Related: Fagged; fagging.
fag (n.1): British slang for "cigarette" (originally, especially, the butt of a smoked cigarette), 1888, probably from fag "loose piece, last remnant of cloth" (late 14c., as in fag-end "extreme end, loose piece," 1610s), which perhaps is related to fag (v.), which could make it a variant of flag (v.).
fag (v.2): "put to work at certain duties, compel to work for one's benefit," 1806, from British public school slang fag (n.) "junior student who does certain duties for a senior" (1785), from fag (v.1). Related: Fagdom (1902); faggery "fatiguing labor" (1853).
fag (n.2): shortening of faggot (n.2) "male homosexual," by 1921. Fag hag "heterosexual woman who keeps company with gay men" attested by 1969.
faggot (n.1): late 13c., "bundle of twigs bound up," also fagald, faggald, from Old French fagot "bundle of sticks" (13c.), of uncertain origin, probably from Italian faggotto "bundle of sticks," diminutive of Vulgar Latin *facus, from Latin fascis "bundle of wood" (see fasces).

Especially used for burning heretics (emblematic of this from 1550s), so that phrase fire and faggot was used to indicate "punishment of a heretic." Heretics who recanted were required to wear an embroidered figure of a faggot on the sleeve as an emblem and reminder of what they deserved.
faggot (n.2): "male homosexual," 1914, American English slang, probably from earlier contemptuous term for "woman" (1590s), especially an old and unpleasant one, in reference to faggot (n.1) "bundle of sticks," as something awkward that has to be carried (compare baggage "worthless woman," 1590s). It may also be reinforced by Yiddish faygele "homosexual" (n.), literally "little bird." It also may have roots in British public school slang noun fag "a junior who does certain duties for a senior" (1785), with suggestions of "catamite," from fag (v.). This also spun off a verb (see fag (v.2).
He [the prefect] used to fag me to blow the chapel organ for him. ["Boy's Own Paper," 1889]
Other obsolete British senses of faggot were "man hired into military service merely to fill out the ranks at muster" (1700) and "vote manufactured for party purposes" (1817).

The explanation that male homosexuals were called faggots because they were burned at the stake as punishment is an etymological urban legend. Burning sometimes was a punishment meted out to homosexuals in Christian Europe (on the suggestion of the Biblical fate of Sodom and Gomorrah), but in England, where parliament had made homosexuality a capital offense in 1533, hanging was the method prescribed. Use of faggot in connection with public executions had long been obscure English historical trivia by the time the word began to be used for "male homosexual" in 20th century American slang, whereas the contemptuous slang word for "woman" (in common with the other possible sources or influences listed here) was in active use early 20c., by D.H. Lawrence and James Joyce, among others.
Fagin (n.): character in "Oliver Twist" (1838); used for "trainer of thieves" by 1842.
fagot (n.): early alternative spelling of faggot (n.1).
fagoting (n.): in embroidery, 1885, from faggot (n.1) "bundle." So called from the threads tied together in the middle.
fagus (n.): botanical genus of beech trees, from Latin fagus "beech," from PIE root *bhagos "beech tree" (source also of Greek phegos "oak," Latin fagus "beech," Russian buzina "elder," Old English bece, Old Norse bok, German Buche "beech"), perhaps with a ground sense of "edible" (and connected with the root of Greek phagein "to eat;" see -phagous). Beech mast was an ancient food source for agricultural animals across a wide stretch of Europe.
The restriction to western IE languages and the reference to different trees have suggested to some scholars that this word was not PIE, but a later loanword. In the Balkans, from which the beech started to spread after 6000 BC, the [Greek] word means 'oak,' not 'beech.' Yet 'oak' and 'beech' are both 'fruit-bearing trees,' so that a semantic shift from 'oak' to 'beech' appears quite conceivable. The word itself may then have been PIE after all. [de Vaan]
Fahrenheit (adj.): temperature scale, 1753, named for Gabriel Daniel Fahrenheit (1686-1736), Prussian physicist who proposed the scale in 1714. The "zero" in it is arbitrary, based on the lowest temperature observed by him during the winter of 1709 in Danzig. An abstract surname meaning literally "experience."
faience (n.): fine kind of pottery or earthenware, 1714, from French faïence (16c.), probably from Fayence, French form of Faenza, city in Italy that was a noted ceramics center 16c. The city name is Latin faventia, literally "silence, meditation," perhaps a reference to a tranquil location.
fail (v.): c. 1200, "be unsuccessful in accomplishing a purpose;" also "cease to exist or to function, come to an end;" early 13c. as "fail in expectation or performance," from Old French falir "be lacking, miss, not succeed; run out, come to an end; err, make a mistake; be dying; let down, disappoint" (11c., Modern French faillir), from Vulgar Latin *fallire, from Latin fallere "to trip, cause to fall;" figuratively "to deceive, trick, dupe, cheat, elude; fail, be lacking or defective." Related: Failed; failing.

Replaced Old English abreoðan. From c. 1200 as "be unsuccessful in accomplishing a purpose;" also "cease to exist or to function, come to an end;" early 13c. as "fail in expectation or performance." From mid-13c. of food, goods, etc., "to run short in supply, be used up;" from c. 1300 of crops, seeds, land. From c. 1300 of strength, spirits, courage, etc., "suffer loss of vigor; grow feeble;" from mid-14c. of persons. From late 14c. of material objects, "break down, go to pieces."
fail (n.): late 13c., "failure, deficiency" (as in without fail), from Old French faile "deficiency," from falir (see fail (v.)). The Anglo-French form of the verb, failer, also came to be used as a noun, hence failure.
fail-safe (adj.): also failsafe, fail safe "safe against failure," 1945, originally in reference to aircraft construction, from fail (v.) + safe (adj.). The novel about a nuclear attack caused by mechanical error is from 1962.
failing (n.): late 14c., "failure;" 1580s, "defect, fault," verbal noun from fail (v.).
failure (n.): 1640s, failer, "a failing, deficiency," also "act of failing," from Anglo-French failer, Old French falir "be lacking; not succeed" (see fail (v.)). The verb in Anglo-French used as a noun; ending altered 17c. in English to conform with words in -ure. Meaning "thing or person considered as a failure" is from 1837.
fain (adj.): Old English fægen, fagen "glad, cheerful, happy, joyful, rejoicing," from a common Germanic root (cognates: Old Saxon fagan, Old Norse feginn "glad," Old High German faginon, Gothic faginon "to rejoice"), perhaps from PIE *pek- (1) "to make pretty." Often "glad" in a relative sense, "content to accept when something better is unobtainable." As an adverb, from c. 1200. Related: Fainly.
faineant (adj.): 1855; earlier as a noun (1610s); from French fainéant (16c.) "do-nothing," from fait, third person singular of faire "to do" (from Latin facere "to make, do;" see factitious) + néant "nothing" (compare dolce far niente). According to OED this is a French folk-etymology alteration of Old French faignant (14c.), present participle of faindre "to feign" (see feign). Applied in French to the late Merovingian kings, puppets in the hands of the palace mayors. Related: Faineance "the habit of doing nothing."
faint (adj.): c. 1300, "enfeebled; wearied, exhausted," from Old French faint, feint "false, deceitful; sham, artificial; weak, faint, lazy, indolent, cowardly," past participle of feindre "hesitate, falter, be indolent, show weakness, avoid one's duty by pretending" (see feign). Also from c. 1300 as "deceitful; unreliable; false." Meaning "wanting in spirit or courage, cowardly" (a sense now mostly encountered in faint-hearted) is from early 14c. From early 15c. of actions, functions, colors, etc., "weak, feeble, poor." Meaning "producing a feeble impression upon the senses" is from 1650s.
faint (v.): c. 1300, "grow weak, become enfeebled," also "lack courage or spirit, be faint-hearted," and "to pretend, feign;" from faint (adj.). Sense of "swoon, lose consciousness" is from c. 1400. Also used in Middle English of the fading of colors, flowers, etc. Related: Fainted; fainting. For Chaucer and Shakespeare, also a transitive verb ("It faints me").
faint (n.): c. 1300, "faintness, faint-heartedness," from faint (adj.). From 1808 as "a swoon."
faint-hearted (adj.): "cowardly, timorous," c. 1400, from faint (adj.) + hearted. Related: Faint-heartedly; faint-heartedness; faint-heart.
faintish (adj.): 1660s, from faint (adj.) + -ish.
faintly (adv.): c. 1300, "dispiritedly, timidly, half-heartedly;" early 14c. "feebly, wearily, without vigor;" from faint (adj.) + -ly (2). Meaning "indistinctly" is from 1580s. Also in Middle English, "deceitfully, hypocritically, falsely" (mid-14c.).
faintness (n.): early 14c., "feebleness, weariness," from faint (adj.) + -ness. Meaning "exhaustion" is mid-15c. Of color, light, etc., from 1640s.