Divisibility Rules Activities

Looking for a fun divisibility rules activity? This collection of free divisibility rules activities and games will make teaching divisibility fun!

Rules of Divisibility

A number is considered to be divisible by a given number if there is no remainder when the two numbers are divided. When working with large numbers, it is often easier to use divisibility tests instead of performing long division by hand.

2: A number is divisible by 2 if the last digit is even (0, 2, 4, 6, or 8).

For example, 48 is divisible by 2 because the last digit of 48 (8) is even.

3: A number is divisible by 3 if the sum of the digits is divisible by 3.

For example, 96 is divisible by 3 because 15 (9 + 6) is divisible by 3.

4: A number is divisible by 4 if the last two digits are divisible by 4.

For example, 124 is divisible by 4 because 24 (the last two digits) is divisible by 4.

5: A number is divisible by 5 if the last digit is 0 or 5.

For example, 1000 is divisible by 5 because the last digit is 0.

6: A number is divisible by 6 if the number is divisible by both 2 and 3.

For example, 72 is divisible by 6 because it is divisible by both 2 and 3. We know 72 is divisible by 2 because its last digit is an even number. We know 72 is divisible by 3 because 9 (7 + 2) is divisible by 3.

8: A number is divisible by 8 if the last three digits are divisible by 8.

For example, 160 is divisible by 8 because the last three digits (160) are divisible by 8 (8*20 = 160).

9: A number is divisible by 9 if the sum of the digits is divisible by 9.

For example, 333 is divisible by nine because 9 (3 + 3 + 3) is divisible by 9.

10: A number is divisible by 10 if the last digit is 0.

For example, 90 is divisible by 10 because the last digit is 0.

Divisibility Rules Reference Tools and Notes

Divisibility Rules Foldable

Journal Wizard shares a fun divisibility rules foldable that you can have students create and glue in their interactive notebooks.

Divisibility Rules Interactive Notebook Page

Hodges Herald used a very creative matchbook fold to create a divisibility rules interactive notebook page.

Divisibility Rules Activities and Puzzles

Divisibility Puzzle

Put your knowledge of divisibility to the test with this fun divisibility puzzle that involves placing the digits 0-9 in the missing spaces.

Divisibility Rules Dice Game

I created this divisibility rules dice game several years ago to give students practice with using divisibility rules. To play the game, students need to be able to determine if numbers are divisible by 2, 3, 5, 9, or 10.

The Is it Possible? Divisibility task challenges students to work together to construct a ten digit number which is divisible by every number from 2 to 18. Your students will get way more practice with this divisibility rules activity than any divisibility rules worksheet you could hand them!

Twelve Envelopes Divisibility Puzzle

I originally created this hands-on version of the twelve envelopes puzzle as a first day of school activity. But, I think it would also make the perfect addition to any divisibility rules unit!

Divisibility Rules Card Game

Idaho State University’s College of Education has a divisibility rules game on their website that uses a deck of playing cards.

Digits Challenge

The New Zealand government has a plethora of curriculum resources available for free online. The Digits Challenge (pdf) shares two different divisibility rules challenges for students to complete involving determining the age of a grandmother and finding a number that meets certain divisibility criteria.

Click the PDF icon once you get to the website to download the activity.

Don Steward Divisibility Activity

Don Steward was a prolific resource creator in the United Kingdom. He wrote a set of excellent divisibility rules activities where students must figure out the digits A and B.