The sum of two numbers is 144 and their HCF is 24. How many such pairs of numbers exist?

Explanation

1. 01

   Write the numbers as 24a and 24b with a and b co-prime.

2. 02

   $24(a + b) = 144$, so $a + b = 6$.

3. 03

   Pairs with sum 6: (1, 5), (2, 4), (3, 3). Only (1, 5) is co-prime.

4. 04

   So there is exactly 1 pair: 24 and 120.