Divisibility Rules

10

A number is divisible by 10 if the units digit is a 0. For example, 0, 490, and -20 are all divisible by 10.

12

A number is divisible by 12 if it's divisible by both 3 and 4. For example, 663 is not divisible by 12 because it's not divisible by 4. 162,480 is divisible by 12 because it's divisible by both 4 (the last two digits, 80, are divisible by 4) and 3 (1 + 6 + 2 + 4 + 8 + 0 = 21, and 21 is divisible by 3).

3

A number is divisible by 3 if the sum of its digits is divisible by 3. This means you add up all the digits of the original number. If that total is divisible by 3, then so is the number. For example, to see whether 83,503 is divisible by 3, we calculate 8 + 3 + 5 + 0 + 3 = 19. 19 is not divisible by 3, so neither is 83,503.

4

A number is divisible by 4 if its last two digits, taken as a single number, are divisible by 4. For example, 179,316 is divisible by 4 because 16 is divisible by 4.

1

All whole numbers are divisible by 1.

11

This one's a bit involved but worth knowing. (Even if it doesn't come up on the test, you can still impress your friends at parties.) Here's how to tell if a number is divisible by 11: Add every other digit starting with the leftmost digit and write their sum. Then add all the numbers that you didn't add in the first step and write their sum. If the difference between the two sums is divisible by 11, then so is the original number. For example, to test whether 803,715 is divisible by 11, we first add 8 + 3 + 1 = 12. To do this, we just started with the leftmost digit and added alternating digits. Now we add the numbers that we didn't add in the first step: 0 + 7 + 5 = 12. Finally, we take the difference between these two sums: 12 - 12 = 0. Zero is divisible by all numbers, including 11, so 803,715 is divisible by 11.

7

7 may be a lucky number in general, but it's unlucky when it comes to divisibility. Although a divisibility rule for 7 does exist, it's much harder than dividing the original number by 7 and seeing if the result is an integer. So if the GRE happens to throw a "divisible by 7" question at you, you'll just have to suck it up and do the math.

2

A number is divisible by 2 if it's even.

5

A number is divisible by 5 if its last digit is 0 or 5. Examples include 0, 430, and -20.

6

A number is divisible by 6 if it's divisible by both 2 and 3. For example, 663 is not divisible by 6 because it's not divisible by 2. But 570 is divisible by 6 because it's divisible by both 2 and 3 (5 + 7 + 0 = 12, and 12 is divisible by 3).

8

A number is divisible by 8 if its last three digits, taken as a single number, are divisible by 8. For example, 179,128 is divisible by 8 because 128 is divisible by 8.

9

A number is divisible by 9 if the sum of its digits is divisible by 9. This means you add up all the digits of the original number. If that total is divisible by 9, then so is the number. For example, to see whether 531 is divisible by 9, we calculate 5 + 3 + 1 = 9. Since 9 is divisible by 9, 531 is as well.