Speed and Accuracy: Divisor Tests

by , Jul 30, 2010

By Guest Author Jordan Schonig

For those of you who didnt know, you cant use a calculator on the GMAT. The following quick tips well help you figure out what a certain number is divisible by. Remember, calculators are not allowed on the test, so these tips may very well help your speed and accuracy.

Divisible by 2:

Any number divisible by 2 ends in 0, 2, 4, 6, or 8 (even numbers).

Divisible by 3:

To determine if a number is divisible by 3, just add up its digits; if the sum of the digits is divisible by 3, then your number is divisible by 3 also. Hint: If your number is so large that the sum of its digits is also too large, just add the digits of the sum and see if this new sum is divisible by 3.

Example: Is 1636668 divisible by 3?

1+6+3+6+6+6+8= 36

3+6=9, which is divisible by 3

Divisible by 4:

If the final two digits of a certain number form a number divisible by 4 OR form a double zero, then the number is divisible by 4. (Hint: Memorize this pattern of two-digit numbers that are divisible by 4: even0, even4, even8, odd2, odd6. By this pattern, I instantly know that numbers like 60, 80, 88, 52, 96, 124, 348, 556, etc, are divisible by 4).

Example: Is 141424 divisible by 4?

Is 24 divisible by 4? Yes, so the number is divisible by 4.

Example: Is 535892800 divisible by 4? Yes, the last two digits are zero.

Divisible by 5:

All numbers divisible by 5 end in either 5 or 0.

Divisible by 6:

All numbers divisible by both 3 and 2. In other words, all even numbers divisible by 3.

Example: Is 20712 divisible by 6?

Is it even? Yes, the number is even, so it is divisible by 2.

2+0+7+1+2=12, which is divisible by 3, which means the number is also divisible by 6.

Divisible by 7:

Much too complicated, in my opinion. I am fairly certain that you are better off just dividing by 7.

Divisible by 8:

A number is divisible by 8 if its last three digits are divisible by 8. Sorry guys, this might not be the most helpful tip, but if you find yourself having to work with a very large number, it will certainly save you time. If anybody else has a divisor test for 8, please post!

Example: Is 7953408 divisible by 8?

Is 408 divisible by 8?

408 / 8 = 51. Yes, the number is divisible by 8.

Divisible by 9:

Divisibility by 9 is tested much the same way you test divisibility by 3. Add the digits; if the sum is divisible by 9, then the number is also.

Example: Is 207 divisible by 9?

2+0+7= 9. Yes, it is.

Divisible by 10:

Ends in 0

Divisible by 11:

This one is pretty awesome. Add up the odd-numbered digits (the 1st, 3rd, 5th, etc) and add up the even-numbered digits (the 2nd, 4th, 6th, etc) and subtract them. If the difference is 0, or if it is divisible by 11, then your number is divisible by 11. (Hint: You can also just alternate signs: e.g. with 352, I can do 3 5 + 2 = 0, or with 7458, I can do 7 4 + 5 - 8 = 0.

Example: Is 5027 divisible by 11?

(5+2) (0 + 7) = 0; yes, its divisible by 11.

While these divisor tests may seem like superfluous information since nearly all of us can perform these operations the old fashioned way, they will save us precious time on the exam. Oh, and after you learn these, dont be afraid to astonish your friends with your amazing mental math abilities.