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Question

If a and b are positive integers such that a = x3y2 and b = xy3, where x, y are prime numbers, then HCF (a, b) = ?

(a) xy
(b) xy2
(c) x2y2
(d) x3y3

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Solution

(b) xy2
It is given that:
a = x3y2 and b = xy3, where x and y are prime numbers
∴ HCF (a, bā€‹) = HCF (x3y2, xy3)
we know,
ā€‹ ā€‹ HCF = Product of smallest power of each common prime factor in the numbers
= xyā€‹2

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