Plural of grandmother; the mothers of your parents, or any older female ancestor.
From 'grand-' (great, of high rank, from Latin 'grandis') plus 'mother' (from Proto-Indo-European 'mater'). The 'grand-' prefix was added in Middle English to distinguish grandparents from parents.
Interestingly, the word 'grandmother' is relatively new to English—in Old English they would have said 'ealra' (eldest mother), and the 'grand-' prefix only started being used regularly around the 1200s when family relationships became formally documented.
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