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find the largest number that divides 2053 and 967 and leaves a remainder of 5 and 7 respectively
Let m be the required number.
Now, on dividing 2053 and 967 by m let the quotients be q1 and q2 respectively,
so, by Euclid 's division lemma,
2053 = mq1 + 5 ---- (i)
967  = mq2 + 7 ---- (ii)
Now, mq1 = 2048 and, mq2 = 960
clearly, hcf of mq1 and mq2 is m
so, m = H.C.F {2048, 960} = 64


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