Question

The product of two numbers is 9126. If HCF of the numbers is 39, find the larger numbers.

Answer 1

Let the numbers 39a and 39b.

Then, 39a x 39b = 9126

=>ab = 6.

Now, the co-primes with product 12 are (1, 6) and (2,3).

[Note: 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 (39 x 1, 39 x 6) and (39 x 2 , 39 x 3).

Clearly, there are 2 such possible pairs.