2. Ways to Check for Divisibility

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

4. Now You Try Are these numbers divisible by 2? a)458 b)1279 c)759 d)555 e)1050

5. 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

6. Dividing by 3 378 For example, take 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 Add up the digits of the number 7+3+8= 18 Is 18 divisible by 3? 1 + 8 = 9 Is 9 divisible by 3?

7. Now You Try Are these numbers divisible by 3? a)639 b)56 c)86 d)360 e)468

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

9. Now You Try Are these numbers divisible by 4? a)584 b)261 c)56 d)920 e)767

10. Dividing by 5 If the number ends in 5 or 0

11. Now You Try Are these numbers divisible by 5? a)554 b)6890 c)345 d)902 e)845

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

13. Now You Try Are these numbers divisible by 6? a)897 b)258 c)630 d)345 e)84

14. 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

15. Dividing by 7 085 For example, take the number If that number is divisible by 7, then the original number is If your sum is still a big number, repeat the process Double the ones digit (2 x 5 = 10) and subtract from the remaining number (8 0) 80 -(2 x5)= 70 Is 70 divisible by 7? 7 – (2 x 0) = 7 Is 7 divisible by 7?

16. Now You Try Are these numbers divisible by 7? a)578 b)398 c)48 d)1903 e)490

17. 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?

18. Now You Try Are these numbers divisible by 8? a)568 b)396 c)48 d)1903 e)490

19. 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

20. Dividing by 9 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 Add up the digits of the number 27 Is 27 divisible by 9? 2 + 7 = 9 Is 9 divisible by 9? For example, take the number 924,561 9+2+4+6+5+1=

21. Now You Try Are these numbers divisible by 9? a)578 b)398 c)48 d)1903 e)490

22. Dividing by 10 If the number ends with a 0

23. Now You Try Are these numbers divisible by 10? a)578 b)398 c)48 d)1903 e)490

24. 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

25. Dividing by 11 For example, take the number 1 3 7 5 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 Identify the positions 1375 13 24 Sum the odd positions 5 + 3 = 8 Sum the even positions 7 + 1 = 8 Subtract 8 - 8 = 0

26. Now You Try Are these numbers divisible by 11? a)578 b)398 c)48 d)1903 e)490

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

28. Now You Try Are these numbers divisible by 12? a)578 b)398 c)48 d)1908 e)420

29. REVIEW 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

30. Assignment Tell what each number is divisible by, either 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 1)186 2)85 3)69 4)298 5)747 11)3870 12)7896 13)69095 14)4892 15)3487 6)952 7)3650 8)2738 9)1132 10)5084