A real root of a number can only be larger than the number if the number is between -1 and +1, and in that range the root itself is limited to -1 to +1. The only way for the 4537'th root of a number to be infinity is if the number itself is infinity, and if that is the case then factoring for roots is not going to produce anything other than infinity.
Factoring can only help if you apply it at the stage of constructing the number whose root is being taken so that it does not reach overflow (represented by infinity.)
Factoring itself is probably not going to work because you are going to run into prime numbers. You should probably instead be looking at log representation.