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If $p = a^{2} x b^{3}$ and $q = a^{3} x b$ , where a and $b$ are distinct primes, then HCF $(p$ , q) is:

Class 10Fundamental Theorem of ArithmeticNumber Systems

A $a^{2} x b$
B $a^{3} x b^{3}$
C $a^{2} x b^{3}$
D $a x b$

Step-by-Step Solution

HCF takes the lowest power of each common prime:

a^{2}

(min of 2 and 3) and

b^{1}

(min of 3 and 1), giving

a^{2} x b

.

Answer: A)

a^{2} x b

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