The definition of relative primality that I was taught was that:
Two numbers are relatively prime if the only common positive factor of the two numbers is one.
Every integer (except zero) divides zero and the only positive factor of one is one. Thus, the only common positive factor of zero and one is one.
Thus, it would seem that zero and one are relatively prime by the definition above. By convention is this not the case? i.e. zero is defined as not being relatively prime with any integer?