The product of two numbers is 2028 and their H.C.F is 13. The number of such pairs is__________?

A. 1
B. 2
C. 3
D. 4

Explanation:

Let the numbers be 13a and 13b.

Then, 13a * 13b = 2028 => ab = 12.
Now, co-primes with product 12 are (1, 12) and (3, 4).
So, the required numbers are (13 * 1, 13 * 12) and (13 * 3, 13 * 4).
Clearly, there are 2 such pairs.