Question

the product of two numbers is 2028 and their HCF is 13 . What is the number of such pairs?

Answer 1

Let the numbers 13a and 13b.

Then, 13a x 13b = 2028

=>ab = 12.

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

[ Two integers a and b are said to be coprime 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 (13 x 1, 13 x 12) and (13 x 3, 13 x 4)

Clearly, there are 2 such pairs.

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Answer 2

Step-by-step explanation:

which is the required solution