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Q.

If two positive integers a and b are written as
a = x2y2 and b = xy2, where x and y are the prime numbers then the HCF(a,b) is:

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a

xy

b

xy2

c

x2y

d

x2y2

answer is B.

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Detailed Solution

Concept- HCF says that the HCF of two numbers is the highest common factor that these numbers can have.
Step 1- we can write given, a = x2y2, as , a = x × x ×y × y……………………(i)
and b = xy2 , as , b = x× y× y…………………………(ii)
Step 2- Now, the maximum common factor that a and b can have will be x× y× y
From equation (i) and equation (ii),
HCF of a and b is xy2.
Hence, the correct answer is option 2) xy2

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