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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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