Can anyone give me some suggestions as to how to go about identifying several moduli for any given positive integer that will produce the smallest residues?

The situation is this:

For any given positive integer of 100 decimal digits

I would like to find 5 moduli, the product of which can represent the 100 digit integer. (Does this mean that each moduli should be about 20 digits long?)

I would like the resultant residues for to be 5 digits or less.