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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