Find Multiples of Three...Fast!

October 17, 2008

There are plenty of GRE quant questions that involve determining whether a number is a multiple of three. Too many students use old-fashioned long division to figure it out, costing themselves time and, often, accuracy.

Fortunately, there's a better way.

Digits and Divisibility Rules

To figure out whether a number is divisible by three, add the digits. (That's it!)

For instance, consider the number 168. Add the digits 1, 6, and 8, and the result is 15. 15 is divisible by 3, so that means 168 is, as well.

If you're dealing with a very large number, the result of adding the digits might be too big. Say you were evaluating 9,846. The sum of the digits is 27. You probably know that 27 is divisible by 3, but if you didn't, you can repeat the process. 2 + 7 = 9, which is a multiple of 3.

It doesn't matter what number you want to test--if you need to know whether something is divisible by three, this is the method to use.

It Works For Nine, Too!

You can use the same approach to determine whether an integer is divisible by 9.

Consider, for example, 153. Add the digits: 1 + 5 + 3 = 9. 9 is divisible by 9, so 153 must be, as well. Like the rule for 3, this works for any integer you wish to test.

There are divisibility rules for many small integers, and I cover all the important ones in my Total GRE Math. Three is probably the easiest and most useful of the bunch.

Jeff Sackmann is a test-prep tutor based in New York City and the author of Total GRE Math, among other GRE and GMAT resources.

Need a better Quant score? Check out Total GRE Math.