Question 6
If two positive integers a and b are written as a=x3y2 and b=xy2 where x, y are prime numbers, then HCF (a, b) is
A) xy
B) xy2
C) x3y3
D) x2y2
The answer B.
Given that, a=x3y2=x×x×x×y×y
b=xy3=x×y×y×y
HCF is the product of the smallest power of each common prime facter involved in the numbers
∴ HCF of a and b = HCF (x3y2,xy3)=x×y×y=xy2