This document outlines divisibility rules for numbers 2 through 12. It provides examples for each rule, showing how to determine if a number is divisible by that factor based on its digits. The rules check properties like the last digit being even, the sum of digits, or the last few digits forming a multiple of the factor. Mastering these rules makes it faster to assess divisibility without calculating the remainder when dividing.

1. Division & RulesBy: Ashley Younts

2. Using the divisibility rules:For each number there is a rule that will help you learn what numbers are divisible by. Stick to the rules!

3. Divisibility by 2If the last digit is even, the original number is divisible by two. ……

4. Example: 916 would be divisible by two because “6” is an even number.

5. 817 wouldn't work because “7” is not an even number.

6. DIVISIBILITYBY3If the sum of the digits is divisible by 3, then the original number is divisible by 3.

7. Example: 2162+1+6=99 is divisible by 3

8. 215would not work because 2+1+5=8 8 is not divisible by 3.215

9. If the last two digits form a number that is divisible by 4, then the original number is divisible by 4. Divisibility by 4

10. Example: 4324& 4325Looking at the last two digits (underlined) you can see which one will be divisible by 4.

11. If the last digit is either 0 or 5, then the original number is divisible by 5. Divisibility by 5

12. Example: 455 works for this one because the last digit is a 5.

13. Even choosing a huge number like, [893,752,075,983] it will not work, because the last digit is a 3.

14. Divisibility by 6If the number is divisible by 2 and 3, then it is divisible by 6.

15. Example: looking at the number 1536, using the rules for both 2 and 3 we see that it checks in both:2: if the last digit is an even number √ yes3: add 1+5+3+6=15 √ yes

16. Now taking a number like 1537, we already know that it will not work because the last digit is not an even number. We have to check both rules for 2 and three because sometimes one will check and the other will not & if one rules fails, you will automatically know that it isn’t going to work. If one rule doesn’t work…

17. Divisibility by 8If the last three numbers are divisible by 8, then the original number is divisible by 8.

18. Example: 13288/328= 41 so this number is divisible by 8. If the number would have had a remainder then the number would not work.

19. If the sum of the digits is divisible by 9, then the number is divisible by 9. Divisibility by 9

20. Example: 216, 2+1+6=9. 217 would not work because 2+1+7=10 and 10 is not divisible by 9.

21. Pay close attention, this rule is tricky!Find the sum of the odd numbered digits, and subtract that number from the sum of the even number digits.Divisibility by 11

22. Example: 7,204,8577+8+0+7=22 & 5+4+2=11 22-11=11So this number is divisible by 11.

23. If the number is divisible by 3 and 4, then it is divisible by 12. Divisibility by 12

24. Example: 3156 3: 3+1+5+6= 15 which is divisible by 3… check4: last two digits are divisible by 4This number is divisible by 12.

25. Now that you have learned some great rules for divisibility, it will make it easier and help take up less time when figuring out if it is divisible by certain numbers. Ending!

26. Thanks to Google Images and Clip art!