Q. 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
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.
