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Divisibility Rules

Our Pre-Algebra tutorial software program contains over 60 topic areas. One of them is Divisibility Rules, and this page summarizes the main ideas of this topic. This page is intended for review, and is not a substitute for the interactive, self-paced tutorials of the MathTutor pre-algebra software program.

General Explanation

In this lesson we will learn to use divisibility rules. Let's review some of the most important ones:
 
  • A number is divisible by 2 if it is an even number.
  • A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9.
  • A number is divisible by 4 if 4 is a factor of the number formed by the last 2 digits of the number.
  • A number is divisible by 5 if the number ends in a 5 or a 0.
  • A number is divisible by 6 if the number has both 2 and 3 as factors.
  • A number is divisible by 8 if 8 is a factor of the number formed by the last 3 digits of the number.
  • A number is divisible by 10 if the number ends in a 0.
Sample Problem 1

Is 162 divisible by 9?

Solution

From the divisibility rules, we know that if a number is divisible by 9 then the sum of its digits is 9.
 
The sum of the digits of 162 is: 1 + 6 + 2 = 9.
 
Since the sum of the digits is divisible by 9, then 162 is divisible by 9.

Sample Problem 2

Is 271 divisible by 10?

Solution

We know that if a number is divisible by 10 it must end in a 0. Since 271 ends in 1, it is not divisible by 10.

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