Question

if two +ve integers a and b are written as a=x³y² and b=xy³, where x, y are prime number, then HCF (a, b) is ​

Answer 1

Answer:

xy ^{2}xy2

Explanation:

a=x3y2

b=xy3

For finding hcf(a,b)

a= x x x y y

b= x y y y

the terms same in both a and b are x y y

x y y = xy2

Hence, HCF(a,b)=

xy ^{2}xy2

Answer 2

Answer:

. xy2

Let a = x3y2 = x × x × x × y × y And

b = xy3 = x × y × y × y

⇒ HCF of a and b = HCF (x3y2, xy3) = x × y × y = xy2 [Since, HCF is the product of the smallest power of each common prime factor involved in the numbers]