Question

If two positive integers a and b are written as a = x³ y² and b = xy³, where x, y are prime numbers, then HCF (a,b) is

A. xy

B. xy²

C. x³y³

D. x²y²

Answer 1

B. xy²

Let a = x³y² = x × x × x × y × y

And b = xy³ = x × y × y × y

⇒ HCF of a and b = HCF (x³y², xy³) = x × y × y = xy²

[Since, HCF is the product of the smallest power of each common prime factor involved in the numbers]