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Find HCF (a, b) where $a = p q 2 and b = p 3 q .$

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p 2 q 2

p 3 q 3

p 3 q 2

answer is D.

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Detailed Solution

Given

a = p q 2 and b = p 3 q

.
Product of two numbers =

LCM × HCF

a = p q 2 and b = p 3 q LCM (a, b) = p 3 q 2

Evaluate products of a and b.

a = p q 2 and b = p 3 q ∴ a × b = p q 2 × p 3 q ⇒ a × b = p 4 q 3

∴

product of two numbers =

LCM × HCF

⇒ p 4 q 3 = p 3 q 2 × H C F

⇒ H C F = p 4 q 3 p 3 q 2 ⇒ H C F = p q

Therefore HCF(a, b)

= p q

.
Hence the correct option is 4.

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