What is the number of integral solutions of the equations HCF(a,b) = 5 and a + b = 65?
- Exactly one
- Infinitely many
- Less than 65
Since HCF (a,b) = 5, let a = 5x and b = 5y
So, 5x + 5y = 65
x + y = 13
So, possible pairs (x,y) are (1,12), (2,11), (3,10), (4,9), (5,8), and (6,7).
So, there are 6 solutions which is less than 65.
The correct option is C.