Question

If two positive integers a and b are written as a = x3y2 and b = xy3 , where x, y are prime numbers, then HCF ( a, b)

Answer 1

It is given that If two positive integers a and b are written as a = x³y² and b = xy³ , where x, y are prime numbers.

             we have to find the value of HCF(a, b),

here a = x³y² = x²(xy²)

and b = xy³ = (xy²)y

     we know HCF means highest common factor. so, find hcf of a and b and get the hcf of a and b.

    here we see highest common factor is xy².

so, HCF(a, b) = xy²

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Answer 2

$\huge\mathcal{Answer:}$

$a = {x}^{3} {y}^{2} \: b = x {y}^{3}$

$a = {x}^{3} {y}^{2} = {x}^{2} (x {y}^{2} )$

$b = x {y}^{3} = (x {y}^{2} )$

$hcf(ab) = x {y}^{2}$