Question

Help Emmi determine the highest number that divides 134 and 167 leaving 2 as the remainder in each case?

Answer 1

The term 'the greatest number that divides' indicates that we need to find the GCD of the given numbers.

However, to adjust the remainder 2, we will find the GCD after subtracting 2 from each of them.

So, we have to find the GCD of (134 – 2) and (167 – 2).

The factors of 132 and 165 are:
165 = 3 × 5 × 11
132 = 2 × 2 × 3 × 11

Taking all the prime factors common, the highest common factor of (165, 132) = 3 × 11 = 33

Hence, the required number is 33.