Question

The largest number that divides 64 and 72 and leave the remainders 12 and 7 respectively, is

(a) 17 (b) 13 (c) 14 (d) 18

Answer 1

Subtract 12 and 7 from 64 and 72 respectively.
64 − 12 = 52
72 − 7 = 65
The required number is the HCF of 52 and 65.
Now
52 = 4 $\text{×}$ 13
65 = 5 $\text{×}$ 13
∴ HCF 52 and 65 = 13
Therefore, the largest number that divides 64 and 72 and leave the remainder 12 and 7 respectively, is 13.
Hence, the correct option is (b).