Question

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

(a) xy (b) xy² (c) x³y³ (d) x²y²

Answer 1

It is given that,
$$\begin{gathered} a=x^3{y}^2=x\times x\times x\times y\times y \\ b=x{y}^3=x\times y\times y\times y \\ \mathrm{HCF}\left(a,b\right)=\mathrm{HCF}\left(x^3{y}^2,x{y}^3\right)=x\times y\times y=x{y}^2 \end{gathered}$$
Hence, the correct answer is option B.