If two positive integers $a$ and $b$
are written as $a = x^{5} y^{3} and b = x^{2} y^{6}; x, y$ are prime numbers, then $H C F$ $(a, b)$ is

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Solution

Given: $a = x^{5} y^{3} and b = x^{2} y^{6}$

$a = x^{2} y^{3} (x^{3}) and b = x^{2} y^{3} (y^{3})$

So, the HCF is $x^{2} y^{3}$ .
Thus, option (d) is correct.

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Question 6
If two positive integers a and b are written as $a = x^{3} y^{2} a n d b = x y^{2}$ where x, y are prime numbers, then HCF (a, b) is

A) $x y$
B) $x y^{2}$
C) $x^{3} y^{3}$
D) $x^{2} y^{2}$

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If two positive integers a and b are written as a=x5y3 and b=x2y6;x,y are prime numbers, then HCF (a,b) is

Given: a=x5y3 and b=x2y6 a=x2y3(x3) and b=x2y3(y3) So, the HCF is x2y3. Thus, option (d) is correct.

If two positive integers $a$ and $b$
are written as $a = x^{5} y^{3} and b = x^{2} y^{6}; x, y$ are prime numbers, then $H C F$ $(a, b)$ is

Given: $a = x^{5} y^{3} and b = x^{2} y^{6}$

$a = x^{2} y^{3} (x^{3}) and b = x^{2} y^{3} (y^{3})$

So, the HCF is $x^{2} y^{3}$ .
Thus, option (d) is correct.