Etymology
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great- 
word-forming element denoting "kinship one degree further removed," early 15c. (in great uncle), from great (adj.), based on similar use of French grand (see grand-). An Old English way of saying "great-grandfather" was þridda fæder, literally "third father;" in early Middle English furþur ealdefader was used (12c.).
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mega- 

before vowels meg-, word-forming element often meaning "large, great," but in physics a precise measurement to denote the unit taken a million times (megaton, megawatt, etc.), from Greek megas "great, large, vast, big, high, tall; mighty, important" (fem. megale), from PIE root *meg- "great." Mega began to be used alone as an adjective by 1982.

High-speed computer stores 2.5 megabits [headline in "Electronics" magazine, Oct. 1, 1957]
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grand- 
a special use of grand (adj.) in genealogical compounds, originally with the sense of "a generation older than," first attested c. 1200, in Anglo-French graund dame "grandmother," also grandsire (late 13c.), from such use of Old French grand-, which perhaps is modeled on Latin avunculus magnus "great uncle." The partly-Englished grandmother, grandfather are from 15c. Other such words in European languages are formed with the adjectives for "old" or "best" (Danish bedstefar) or as diminutives or pet names (Greek pappos, Welsh taid). The French formation also is the model for such words in German and Dutch. Spanish abuelo is from Latin avus "grandfather" (from PIE *awo- "adult male relative other than the father;" see uncle), via Vulgar Latin *aviolus, a diminutive or adjective substitution for the noun.

The extension of the sense to corresponding relationships of descent, "a generation younger than" (grandson, granddaughter) is from Elizabethan times. The inherited PIE root, *nepot- "grandchild" (see nephew) has shifted to "nephew; niece" in English and other languages (Spanish nieto, nieta). Old English used suna sunu ("son's son"), dohtor sunu ("son's daughter").
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