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Two positive integers a and $b$ can be written as $a = p^{3} q^{2}$ and $b = p q^{3}$ , where $p$ and $q$ are distinct primes.
What is HCF(a, b)?

Class 10HCF and LCMNumber Systems

A $p q^{2}$
B $p^{3} q^{3}$
C $p^{3} q^{2}$
D $p^{4} q^{5}$

Step-by-Step Solution

HCF takes the lowest power of each common prime:

p^{m}

in(3,1) =

p, q^{m}

in(2,3) =

q^{2}

. So HCF =

p q^{2}

.

Answer: A)

p q^{2}

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