Question

Match the following pairs of numbers with their greatest common divisors.

Number pairs	GCD
(i) 27, 36	(a) 12
(ii) 48, 60	(b) 9

• A. (i) and (a), (ii) and (b)
• B. (i) and (b), (ii) and (a)
• C. (i) and (b), (ii) and (b)
• D. (i) and (a), (ii) and (a)

Answer 1

The correct option is B (i) and (b), (ii) and (a)

We can find the greatest common divisor using prime factorization method.

The prime factorization of 27 is:
3 × 3 × 3
The prime factorization of 36 is:
2 × 2 × 3 × 3

Thus, the greatest common divisor is:
3 × 3 = 9

The prime factorization of 48 is:
2 × 2 × 2 × 2 × 3
The prime factorization of 60 is:
2 × 2 × 3 × 5

Thus, the greatest common divisor is:
2 × 2 × 3 = 12

Hence, we match the columns as (i) and (b), (ii) and (a).