Infinity isn't it? Anything divided by 1 just stays the same.
Unless you mean 1 over infinite, in which case the answer is zero. Think about it. If you have a cake and you divide it into 4 pieces, it is tasty (1/4). If you divide it into a thousand pieces you won't taste it (1/1000). As you divide it into more and more pieces the slices will get thinner and thinner. I know this sounds absurd but eventually the slice will be infinitesimally small, in which case you can assume it has disappeared and is pretty much zero (1/infinite).
To senshis the point of 1/infinite = 0 is that the number is so small that it is mathematically irrelevant. It doesn't matter that this number exists and is not zero, what matters is that it doesn't affect our calculations. If you don't assume this, then all of the proofs of calculus simply collapse. Calculus is the study of change, particularly at an infinitesimal level.