Question

If two positive integers $a$ and $b$are written as $a=x^3{y}^2$ and $b=x{y}^3$where$x,y$are prime numbers, then find the HCF of $a$ and$b$.

Answer 1

Solve for the H.C.F of the given two variables.

We are given,

$$\begin{gathered} a=x^3{y}^2=\left(x\right)\times \left(x\right)\times \left(x\right)\times \left(y\right)\times \left(y\right) \\ b=x{y}^3=\left(x\right)\times \left(y\right)\times \left(y\right)\times \left(y\right) \end{gathered}$$

Since $a,b$are positive integers and $x,y$ are prime numbers, we can get the HCF as,

$$\begin{gathered} H.C.F(a,b)=\left(x\right)\times \left(y\right)\times \left(y\right) \\ \Rightarrow H.C.F(a,b)=x{y}^2 \end{gathered}$$

Hence, the required answer is $H.C.F(a,b)=x{y}^2$