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

Question: The product of two numbers is 2028, and their H.C.F is 13. The number of such pairs is:

Solution:
Let,
The two numbers be x and y
Here, xy = 2028

Also 13 is their HCF, thus both numbers must be divisible by 13.
So, let x = 13a and y = 13b,

then
⇒ 13a × 13b = 2028
⇒ 169ab = 2028
⇒ ab = 2028/169
∴ ab = 12

Therefore, required possible pair of values of x and y which are prime to each other are (1, 12) and (3, 4).
Thus, the required numbers pairs are (13, 156) and (39, 52).
The number of possible pairs is 2.