GMAT Divisibility Rules

Early in your GMAT prep for the Quantitative section, it is important to learn the rules of divisibility. The shorthand version is below:

In order to be divisible by …

2 … the number is even

3: the sum of the digits are divisible by 3; i.e. 348 sums to 3 + 4 + 8 = 15, which indicates that 348 is divisible by 3

4: the last two digits are divisible by 4, or the number has two factors of 2; i.e. 2044 is divisible by 4 since the last two digits 44 are divisible by 4. Alternatively, you could do a factor tree on 2044 and see that it has 2 unique factors of 2

5: the number ends in 5 or 0

6: the number has both 2 and 3 as a factor

7: there is no easy rule; best to use “mental math”

8: the number has three factors of 2

9: the number has two factors of 3

10: the number ends in 0, or the number has both 2 and 5 as a factor

GMAT Divisibility Rules and Number Properties

The divisibility rules are very important, since they are used in difficult Number Properties questions. Here are a couple important rules:

Whenever is the GMAT asks:

Is the integer x divisible by y?

It’s really asking:

Does x have y as a factor?

For example, if the question asks:

Is x divisible by 8?

The question is really asking:

Does x have 8 as a factor? (Or, does x have 3 factors of 2?)

Consider the following data sufficiency problem:

Is x divisible by 8?

(1) x is divisible by 4

(2) 5x is divisible by 8

The question is really asking, can we prove x has 3 factors of 2?

Statement 1 proves that x has only 2 factors of 2; thus, it is insufficient.

Statement (2) tells us that 5x has 8 as a factor. This proves that x itself must have 3 factors of 2. The coefficient 5 provides an extra factor of 5, but that doesn’t affect x’s divisibility by 8.  Thus, statement 2 is sufficient and the answer is B.

Alternatively, you could list out possible values of x for both statements:

(1) x could 4, 8, 12, 16, etc. Thus, it may or may not by divisible by 8; insufficient

(2) x could be 8, 16, 24, 32, etc. All of these values are divisible by 8; sufficient

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