[2] The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

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The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

Explanation:

Let the numbers 13$ a $ and 13$ b $.

Then, 13$ a $ x 13$ b $ = 2028

$\Rightarrow$ ab = 12.

Now, the co-primes with product 12 are $\left(1, 12\right)$ and $\left(3, 4\right)$.

[Note: Two integers $ a $ and $ b $ are said to be co-prime or relatively prime if they have no

common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]

So, the required numbers are $\left(13 \times 1, 13 \times 12\right)$ and $\left(13 \times 3, 13 \times 4\right)$.

Clearly, there are 2 such pairs.

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