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

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

A) \[xy\]

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

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

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

Correct Answer: B

Solution :

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

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

\[\therefore \] HCF of a and

\[b=HCF({{x}^{3}}{{y}^{2}},x{{y}^{3}})=x\times y\times y=x{{y}^{2}}\]