Is the prime factorization problem not an instance of the change making problem?

When using as the set of coins all logarithms of the prime numbers or numbers in general, and when using the logarithm of the number to be factored. The problem is just finding the logarithms that can be used to make the total. But then the change making problem is listed as non NP problem, but the prime factorization problem is found to be NP complete. Can anyone explain why this is?

When using as the set of coins all logarithms of the prime numbers or numbers in general

The change-making typically assumes a finite set of coins.

You can, of course, extend it to infinite sets of coins but then you get a different problem. Depending on the exact formulation, it seems plausible that integer factorization would reduce to that new problem.

But then the change making problem is listed as non NP problem, but the prime factorization problem is found to be NP complete.