Question:
If two positive integers a and b are written as a = x3y2 and b = xy3, wfiere x, y are prime numbers, then HCF (a, b) is
(a) xy
(b) xy2
(c)x3y3
(d) xy2
Solution:
(b) Given that, $\quad a=x^{3} y^{2}=x \times x \times x \times y \times y$
and $\quad b=x y^{3}=x \times y \times y \times y$
$\therefore$ HCF of $a$ and $b \quad=\operatorname{HCF}\left(x^{3} y^{2}, x y^{3}\right)=x \times y \times y=x y^{2}$
[since, HCF is the product of the smallest power of each common primè facter involved in the twimbers]
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