The sum of two numbers is 36 and their HCF is 4. How many pairs of such numbers are possible ?

3 4 2 1

3

Let, the numbers are 4x and 4y ATQ, ⇒ 4x + 4y = 36 ⇒ 4(x + y) = 36 ⇒ x + y = 9 ⇒ (1, 8) ⇒ (2, 7) ⇒ (4, 5) We can see the 3 possible pairs.