10th Class Mathematics Real Numbers Question Bank MCQs - Real Number

If two positive integers a and b are written as \[a={{x}^{3}}{{y}^{2}}\] and \[b=x{{y}^{3}}\], where x, y are prime numbers, then HCF (a, b) is

A) xy

B) \[x{{y}^{2}}\]

C) \[{{x}^{3}}{{y}^{3}}\]

D) \[{{x}^{2}}{{y}^{2}}\]

Correct Answer: B

Solution :

Given that, \[a={{x}^{3}}\,{{y}^{2}}=x\times x\times x\times y\times y\]

and \[b=x{{y}^{3}}=x\times y\times y\times y\]

\[\therefore\]HCF of a and \[b=HCF\left( {{x}^{3}}{{y}^{2}},\,x{{y}^{3}} \right)\]

\[=x\times y\times y=x{{y}^{2}}\]

[since, HCF is the product of the smallest power of each common prime facter involved in the numbers]