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प्रश्न
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 ______.
विकल्प
xy
xy2
x3y3
x2y2
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उत्तर
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]
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