Is Zero a factor of Itself

There is no universal agreement on this, some sources say that 0 is a factor of 0 while other sources say that 0 is not a factor of any number, including 0. In my opinion, 0 should be considered as a factor of 0. If you try to apply the first definition with a = 0, notice that you don't get some non-integer quotient, you get nothing at all. Do not make the mistake of thinking that there is a number called "undefined" lurking somewhere on the number line. There is not, it means that that operation is not defined. So you can't even use the first definition to test whether 0 is a factor of 0. On the other hand, you can define a factor as "a is called a factor of b if there exists some integer k such that b = a * k". You can apply this definition with a = b = 0 and the conclusion will be that 0 is a factor of 0. However, as I mentioned earlier, there is no general consensus on this issue. I don't think GMAT will ever give you a question where you need to know whether 0 is a factor of 0 to answer it.