Question

SECTION A
Section A consists of 20 questions of 1 mark each.

1. If two positive integers $a$ and $b$ are written as $a=x^3{y}^{2}andb=x{y}^2$ where $x,y$ are prime numbers, then HCF $(a,b)$ is

• A. $x{y}^2$
• B. $x^2{y}^2$
• C. $xy$
• D. $x^3{y}^3$

Answer 1

The correct option is A $x{y}^2$

Factorize $x^3{y}^2$ and $x{y}^2.$
$x^3{y}^2=x.x.x.y.y$
$x{y}^2=x.y.y.y$
The HCF is the product of the smallest power of each common prime factor involved in the numbers.
The smallest power of each common prime factor is $x$ and $y^2.$
Therefore, the HCF is $x{y}^2.$
The HCF is $x{y}^2$.
Hence, option (B) is correct.