Question

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

Options

• xy

• xy²

• x³y³

• x²y²

Answer 1

If two positive integers a and b are written as a = x³ y² and b = xy³; x, y are prime numbers, then HCF (a, b) is xy².

Explanation:

Given that, 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]