If two positive integers a and b are a x ³y² and b xy³ where x and y are prime then HCF a b is

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If two positive integers a and b are written as a = x 3 y 2 and b = xy 2 where x , y are prime numbers, then HCF a , b isA. XyB. x y2C. x3 y3D. x2 y2

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Q. If two positive integer a and b are written as a = x 3 y 2 and b = xy 3 ; x and y are prime numbers, then find the HCF a , b .

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If two positive integers a and b are written as a = x3 y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is ______.

If two positive integers a and b are written as a = x3 y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is xy2.

Explanation:

Given that, 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]

Concept: Fundamental Theorem of Arithmetic

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