Question

The greatest number which divides 134 and 167 leaving 2 as remainder in each case is
(a) 14
(b) 17
(c) 19
(d) 11

Answer 1

(d) 11
Since we need 2 as the remainder, we will subtract 2 from each of the numbers.
167 − 2 = 165
134 − 2 = 132
Now, any of the common factors of 165 and 132 will be the required divisor.
On factorising:
165 = 3 × 5 × 11
132 = 2 × 2 × 3 × 11
Their common factors are 11 and 3.
So, 11 is the required divisor.