Let the numbers 17a and 17b.
Then, 17a x 17b = 3468
=> ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[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 (17 x 1, 17 x 12) and (17 x 3, 17 x 4).
Clearly, there are 2 such pairs.