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If there is a remainder of 2 then number will divide 2 less than 110 (= 108) and 128 (=126) and be the largest such number. Thus need the hcf of 108 and 126:

108 = 22 x 33

126 = 2 x 32 x 7

hcf = 2 x 32 = 18

Thus 18 is the greatest number which will divide 110 and 128 with a remainder of 2 in each case.

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Q: What is the greatest number which will divide 110 and 128 leaving a remainder 2 in each case?
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