Find the largest no which divided 2053 and 967 and leaves a remainder of 5 and 7 respectively

Find the largest no which divided 2053 and 967 and leaves a remainder

1.	Find the largest no which divided 2053 and 967 and leaves a remainder of 5 and 7 respectively
Answer» 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 = 960clearly, H.C.F. of mq1 and mq2 is mso, m = H.C.F {2048, 960} = 64