factorization

And whats the motivation for doing so - hat would be the benefit?
Using a numeric solve block would limit the precision of the numbers to be used significantly and there seems to be no reason for using the symbolic "solve" as long as we have "factor".

To factor numbers in pure numeric mode you would have to write your own program - but the limitation of precision remains the same as long as you evaluate it numerically.

A numerical solution block and Prime at all are not made for dealing with number theoretic problems. An old program like Derive sure would to a better job here as it brings along a lot of useful functions for that purpose and AFAIK there also exist specialized software.

In Prime you could also play around with constraints like x=trunc(x) instead of "x in Z" or "x=integer", but I doubt that you will have success.