[eigenket]

I don't think there's any interesting difference with different bases. Usually the base you represent stuff in is a relatively small number (because using very large bases is already wildly inefficient). I think it only usually makes sense to consider constant or logarithmic bases. If your base is scaling linearly with your number then things are going to be weird.

The problem of finding factors is only complex when you're asking about relatively big factors. If you're looking for constant or log sized factors you can just do trial division and find them.