Question

The greatest number which divides 134 and 167 leaving 2 as remainder in each case is
(a) 14
(b) 19
(c) 33
(d) 17

Answer 1

First we subtract the required remainder from 134 and 167.
Thus, we will get 132 and 165.
132 = 2 × 2 × 3 × 11 = 2² × 3 × 11
165 = 3 × 5 × 11 = 3¹ × 5 × 11
HCF = 3 × 11 = 33
Thus, the greatest number which divides 134 and 167 leaving 2 as remainder in each case is 33
Hence, the correct answer is option (c).