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(B) Let the two numbers be $x$ and $y$.Given that the product $x 	imes y = 2028$ and the $HCF = 13$.Since $HCF$ is a factor of both numbers,we can wr

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$2$

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(B) Let the two numbers be $x$ and $y$.Given that the product $x 	imes y = 2028$ and the $HCF = 13$.Since $HCF$ is a factor of both numbers,we can write $x = 13a$ and $y = 13b$,where $a$ and $b$ are coprime numbers (i.e.,$gcd(a, b) = 1$).Substituting these into the product equation: $(13a) 	imes (13b) = 2028$.$169 	imes ab = 2028$.$ab = \frac{2028}{169} = 12$.Now,we find pairs of factors $(a, b)$ such that their product is $12$ and they are coprime:$1$. $(1, 12)$ where $gcd(1, 12) = 1$.$2$. $(3, 4)$ where $gcd(3, 4) = 1$.Note: $(2, 6)$ is not considered because $gcd(2, 6) = 2 
eq 1$.Thus,there are $2$ such pairs of numbers.

The product of two numbers is $2028$ and their $HCF$ is $13$. The number of such pairs is

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