HCF Q36

36..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

Answer : [B]

Explanation :

Let the numbers be 13a and 13b. Then, 13a x 13b = 2028  ab = 12.

Now, co-primes with product 12 are (1, 12) and (3, 4).

So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4)

Clearly, there are 2 such pairs.