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# If two positive integers $a$ and $b$ are written as $a = x^3y^2$ and $b = xy^3; x, y$ are prime numbers, then HCF $(a, b)$ is

**(A)** $xy$

**(B)** $xy^2$

**(C)** $x^3y^3$

**(D)** $x^2y^2$

Given:

Two positive integers $a$ and $b$ are written as $a = x^3y^2$ and $b = xy^3; x, y$ are prime numbers.

To find:

Here we have to find HCF $(a, b)$.

Solution:

We know that,

HCF is the product of the smallest power of each common prime factor involved in the numbers.

$a = x^3y^2$

$= x \times x^2\times y^2$

$b = xy^3$

$= x \times y^2 \times y$

Therefore,

HCF of $a$ and $b$ is,

HCF $(x^3y^2, xy^3) = x \times y^2$

$= xy^2$

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