Is 0 (zero) to be Considered as a Multiple of Every Number?

Question: Is 0 (zero) to be considered as a multiple of every number?

Is 0 (zero) to be considered as a multiple of every number?” is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. This particular GMAT data sufficiency question assesses candidates’ critical thinking and hypervigilance. An abstract problem-solving question is mainly given and most of the difficulty comes from obtuse or clever wording, candidates usually miss it.

Case 1:

An integer a is a multiple of an integer bb means that ab = integer: so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer.

Also on the GMAT when we are told that a is divisible by b (or which is the same: "a is multiple of b", or "b is a factor of a"), we can say that:

1. a is an integer;
2. b is an integer;
3. a*b = integer

Hence, it is clear that zero is a multiple of every integer.

Case 2:

Of every integer, 0 is a multiple, thus yes. The key to the GMAT is to carefully read what kind of multiples are requested. Therefore, even though zero is a multiple of every integer, it is not a multiple of any number in a positive way. The GMAT typically uses the phrase "positive multiples of" or some other clarifying language to indicate that they don't want you to consider zero as a multiple (though I can't promise that).

Another point to keep in mind is that while zero is a multiple of every other number, it is not a factor of any other number. There is no other number that might have a zero as a factor because any integer multiplied by zero equals zero. To put it another way, zero cannot be one of a number's factors in order for it to not be zero.

Hence, 0 is a multiple of every integer.

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