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Old English clut "lump of something," also "patch of cloth put over a hole to mend it," from Proto-Germanic *klutaz (cf. Old Norse klute "kerchief," Danish klud "rag, tatter," Frisian klut "lump," Dutch kluit "clod, lump"); perhaps related to clot (v.).
In later use "a handkerchief," also "a woman's sanitary napkin." Sense of "a blow" is from c.1400 early 14c., from the verb. Sense of "personal influence" is 1958, on the notion of "punch, force."
"to beat, strike," early 14c., from clout (n.), perhaps on the notion of hitting someone with a lump of something, or from the "patch of cloth" sense of that word (cf. clout (v.) "to patch, mend," mid-14c.). Related: Clouted; clouting.