It doesn't produce the output you wanted ...
As I mentioned in 482012, the exact reduction isn't important. The results of your 3 manual steps (33,5)(2,4,23) and my 5 manual steps (33,5)(8,23) are completely equivalent.
Adding a dependancy upon Inline::C is heavier than Math::Pari, though GCD could be written in perl of course.
Your algorithm certainly works. However, using GCD requires multiple, O(m*n) passes over the datasets. hv's prime factors approach eliminates the multiple passes and seems, on the small sets I've tried, to get the results more quickly, even with pure perl factoring code.
Coming up with an efficient, pure perl implementation of prime factorisation (limiting myself to integers 0 .. 2**32 ) is my current fun challenge :)