Factoring a large number[say of 400 digits] containing exactly two prime factors is a formidable task. Now ,suppose we change the base to 10000. That is is instead of using the decimal system we use another system with base/radix 10000. This will reduce the number of digits but the number system itself will become unwieldy because of the huge number of digits[0-9999]. One has to go through the tedious task of formulating "simple" multiplication tables for this number system Having done all that, will the task of factorizing a composite number consisting of two primes become easier on a microprocessor?
Taking this to an extreme shows, at least, that for there to be any hope of such a method working, the method must depend both on "large number of digits" (400 in your case) and size of base (10000 in your case). For if the base is larger than the number to be factored, the relevant entry in the multiplication table (there's only one...) isn't going to be of any help to you.