Divisibility Rules: 2, 3, 4, 5, 6, 7, 9, 10,11,13 and higher primes

After the children became factor masters last week, we introduced a set of divisibility rules for the numbers 2, 3, 5, 6, 9, and 10 for the younger children since these rules are easy to learn and apply to any number. See these rules below:

2: last digit of number is 0, 2, 4, 6, or 8

5: last digit of number is 0 or 5

10: last digit of number is 0

3: add the digits and if the sum is a multiple of 3 such as 3, 6, 9, 12, 15, 18..

9: if the sum of the digits is a multiple of 9, such as 9, 18, 27…

6: if the number is divisible by 2 (even) and 3 (sum of digits 3, 6, 9,)


With grades 3 and above, I introduced the divisibility rules for the numbers 4, 8, 7, and 11. 

These rules are much more challenging but so much fun to apply.


4: The last two digits are divisible by 4.

8: The last three digits are divisible by 8.

7: The last digit is multiplied by 2 and subtracted from the rest of the number. The result is either 0 or divisible by 7.

11: The sum of the even digits is subtracted from the sum of the odd digits. The result is either 0 or divisible by 11.


For my most advanced mathematicians, I showed them how I developed divisibility rules for 13, 17, 19 and any prime number by removing the last digit and multiplying it by a constant factor and either subtracting from or adding to the remaining digits (for example, the rule for 13 is to multiply the last digit by 9 and subtracting it from the remaining digits or multiplying the last digit by four and adding it to the remaining digits).



Have fun exploring these rules and then make your own numbers and find divisibility for each.

Divisibility_Rules_2356910_K-3.pdf2.2 MB
Divisibility_Rules_234567891011_3-6thgrade.pdf1.99 MB
Divisibility_Rules_Prime_Numbers_over_11.pdf57.22 KB