Ways to Check for Divisibility

1. Divisibility Rules Ways to Check for Divisibility

2. Dividing by 2 • All even numbers are divisible by 2 • Even numbers are numbers that end with either 2, 4, 6, 8, or 0

3. Now You Try • 458 • 1279 • 759 • 555 • 1050 Are these numbers divisible by 2?

4. Dividing by 3 • Add up the digits of the number • If that number is divisible by 3, then the original number is • If your sum is still a big number, continue to add the digits

5. 7 3 8 • For example, take the number 7 + 3 + 8 = Dividing by 3 • Add up the digits of the number 18 • If that number is divisible by 3, then the original number is Is 18 divisible by 3? • If your sum is still a big number, continue to add the digits 1 + 8 = 9 Is 9 divisible by 3?

6. Now You Try • 639 • 56 • 86 • 360 • 468 Are these numbers divisible by 3?

7. Dividing by 4 • If the last 2 digits together are divisible by 4

8. Now You Try • 584 • 261 • 56 • 920 • 767 Are these numbers divisible by 4?

9. Dividing by 5 • If the number ends in 5 or 0

10. Now You Try • 554 • 6890 • 345 • 902 • 845 Are these numbers divisible by 5?

11. Dividing by 6 • If the number is divisible by 2, and . . . • If the number is divisible by 3

12. Now You Try • 897 • 258 • 630 • 345 • 84 Are these numbers divisible by 6?

13. Dividing by 7 • Double the ones digit and subtract from the remaining digits • If that number is equal to zero or divisible by 7, then the original number is • If your number is still a big number, repeat the process

14. 8 0 5 • For example, take the number 80 - (2 x 5) = Dividing by 7 • Double the ones digit (2 x 5 = 10) and subtract from the remaining number (8 0) 70 • If that number is divisible by 7, then the original number is Is 70 divisible by 7? • If your sum is still a big number, repeat the process 7 – (2 x 0) = 7 Is 7 divisible by 7?

15. Now You Try • 578 • 398 • 48 • 1903 • 490 Are these numbers divisible by 7?

16. Dividing by 8 • If the last three digits are divisible by 8 • If the number is divisible by 2, • then by 2 again, and then by 2 again • So what type of number does it have to be?

17. Now You Try • 568 • 396 • 48 • 1903 • 490 Are these numbers divisible by 8?

18. Dividing by 9 • Similar to dividing by 3 • Add up digits • If that number is divisible by 9 then your number is divisible by 9

19. 6 9 + + 5 2 + + 4 1 = + Dividing by 9 • For example, take the number 924,561 • Add up the digits of the number 27 • If that number is divisible by 3, then the original number is Is 27 divisible by 9? • If your sum is still a big number, continue to add the digits 2 + 7 = 9 Is 9 divisible by 9?

20. Now You Try • 578 • 398 • 48 • 1903 • 490 Are these numbers divisible by 9?

21. Dividing by 10 • If the number ends with a 0

22. Now You Try • 578 • 398 • 48 • 1903 • 490 Are these numbers divisible by 10?

23. Dividing by 11 • Sum the odd positioned digits • Sum the even positioned digits • Subtract • If the difference is zero or divisible by 11, then your number is divisible by 11 • Repeat if needed

24. Dividing by 11 • For example, take the number 1 3 7 5 • Identify the positions 3 1 Sum the odd positions 5 + 3 = 8 1375 Sum the even positions 7 + 1 = 8 4 2 Subtract 8 - 8 = 0 • If that number is zero or divisible by 11, then the original number is • If your sum is still a big number, repeat the process

25. Now You Try • 578 • 398 • 48 • 1903 • 490 Are these numbers divisible by 11?

26. Dividing by 12 • If the number is divisible by 3, and . . . • If the number is divisible by 4

27. Now You Try • 578 • 398 • 48 • 1908 • 420 Are these numbers divisible by 12?

28. Divisible by 2 Divisible by 3 Divisible by 4 Divisible by 5 Divisible by 6 Divisible by 7 Divisible by 8 Divisible by 9 Divisible by 10 Divisible by 11 Divisible by 12 REVIEW

29. Assignment Tell what each number is divisible by, either 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 • 3870 • 7896 • 69095 • 4892 • 3487 • 186 • 85 • 69 • 298 • 747 • 952 • 3650 • 2738 • 1132 • 5084

30. That's all Folks!