How would I go about proving that for all n belonging to the natural numbers, if any given odd number n is divided by 2, then the remainder is *at least* 1? 

I got a hint: Try to reduce the number of n, but I have no idea how that would help.

I was thinking along the lines of induction, but what would be the best approach to this? I just want hints, please. I want to solve this myself, just need a heads up on where to get started.