question_answer

The greatest number which can divide 1354, 1866 and 2762 leaving the same remainder 10 in each case, is

A) 64

B) 124

C) 156

D) 260

Correct Answer: A

Solution :

[a] Required number = HCF of \[(1354-10),\,(1866-10)\] and \[(2762-10)\] = HCF of 1344, 1856, 2752 = HCF of \[({{2}^{6}}\times 3\times 7),\]\[({{2}^{6}}\times 29),\]\[({{2}^{6}}\times 43)={{2}^{6}}=64\]