Divisibility Patterns

Divisibility Patterns will help sixth grade students in our upcoming Fractions units.  Practice these at home, they really work!  They are like little math tricks!

The following rules will help students determine if a number is divisible by 2, 3, 5, 6, 9, or 10.

A number is divisible by:

• 2 if the ones digit is divisible by 2 or even.
• 3 if the sum of the digits is divisible by 3.
• 5 if the ones digit is 0 or 5.
• 6 if the number is divisible by 2 and 3.
• 9 if the sum of digits is divisible by 8.
• 10 if the ones digit is 0.

Here is an example of the work students can do in their head to know what numbers work:

Is 1,120 divisible by 2, 3, 5, 6, 9, or 10?

• 2: YES, The ones digit 0 is divisible by 2.
• 3:  NO.  1 + 1 + 2 + = 4.  You can not divide 4 by 3.
• 5:  YES.  The ones digit is 0.
• 6:  NO. The number is divisible by 2, but not by 3.
• 9:  NO.  The sum of the digits is 4.  4 is not divisible by 9.
• 10:  YES.  The ones digit is 0.  

1,120 is divisible by 2, 5, and 10.