Question

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

Answer 1

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

Given that, $a=x^3{y}^2=x\times x\times x\times y\times y$
$b=x{y}^3=x\times y\times y\times y$

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

$\therefore$ HCF of a and b = HCF $(x^3{y}^2,x{y}^3)=x\times y\times y=x{y}^2$