The sum of two numbers is 156 and their HCF is 13. The numbers of such number pairs is  

Given:

Sum of the numbers = 156

H.C.F of numbers = 13

Concept used:

If the H.C.F of two numbers is H, then the numbers are Hx and Hy. Where x and y are relatively prime numbers or coprimes.

Calculation:

Let numbers are 13x and 13y, where x and y are coprime

Now, 13x + 13y = 156

⇒ 13 (x + y) = 156

⇒ x + y = 156/13 = 12

∴ possible values if x and y are

(x = 1, y = 11)

(x = 5, y = 7)