The best way to get a multiplicitive view of numbers is to transform multiplication into a special form of addition. One of the more general forms of this is t

The best way to get a multiplicitive view of numbers is to transform multiplication into a special form of addition. One of the more general forms of this is the logarithm. The defining equation of the logarithm is that log(a*b) = log(a) + log(b). This turns multiplication into a nice linear addition problem. A less general but more powerful transformation exists on the integers. You can factorize any integer into it's prime factors, then multiply by adding together the powers on matching primes. This may seem like more effort for a similar result, but the prime factors of an integer tell you a lot about that integers divisibility, so it's worth the effort. If you're talking about the interplay between multiplication and addition: Get a degree in pure maths, learn lots of number theory, and cry at how inelegant it is. Trust me, I did it in a past life