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# Divisibility

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1. Divisibility Rules

2. What is Divisibility? • Divisibility means that after dividing, there will be No remainder.

3. Can you tell by just looking at this number if it is divisible by 2? by 5? by 10? by 3 ? by 9? By 6? The divisibility rules can help YOU! 356,821

4. Divisibility Ruleshelp you learnshortcutsto tell when a number can be divided by another number with NO REMAINDER.

5. Dividing By 1 • All numbers are divisible by 1

6. Now You Try • 578 • 1201 • 465 Are these numbers divisible by 1?

7. Dividing by 2 • All even numbers are divisible by 2 • Even numbers are numbers that • end with either 2, 4, 6, 8, or 0 18 ÷ 2 = 9 22 ÷ 2 = 11 Notice that both of these numbers are even. 21 ÷ 2 = 10 R1 NOT EVEN

8. Now You Try • 458 • 1279 • 759 Not an evennumber Not an evennumber Are these numbers divisible by 2?

9. Dividing by 3 A number is divisible by 3 if the sum of the digits is divisible by 3. Is the number 135 divisible by 3? Add the digits: 1 + 3 + 5 = 9 Yes, 135 is divisible by 3 because the sum of the digits is divisible by 3.

10. Now You Try Sum of 6+3+9 =18 • 639 b) 56 Sum of 5+6 =11NO Are these numbers divisible by 3? Sum of 7+3+8 =18 c) 738

11. Dividing by 4 • If the last 2 digits together are divisible by 4 • or take your number, divide it by 2. Then divide that answer by 2, and if you get an EVEN NUMBER then it is divisible by 4 Example 384 21 4) 84 180 EVEN 90 EVEN Example 360 2) 2) 360 180

12. Now You Try 21 • 584 • 261 4) 84 Are these numbers divisible by 4? 15 r1 NO 4) 61 Take the last 2 digits and divide by 4

13. Dividing by 5 • If the number ends in 5 or 0 • 25 ÷ 5 = 5 • 23 ÷ 5 = 4 R3 NO

14. Now You Try • 554 • 6890 • 345 Are these numbers divisible by 5?

15. Dividing by 6 • If the number is divisible by 2, • AND . . . • If the number is divisible by 3

16. Now You Try • 897 • 258 • 630 No it is not EVEN Are these numbers divisible by 6? EVEN, Sum of 2+5+8 =15 EVEN, Sum of 6+3+0 =9

17. Dividing by 7 • There is no special rule to help you know if a number is divisible by 7…

18. Now You Try • 500 • 49 • 2100 Are these numbers divisible by 7?

19. 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? • A number that has been cubed.

20. Now You Try 284 Even 142 Even 71 • 568 2) 2) 2) 568 284 142 Are these numbers divisible by 8? 198 Even 99 Odd NO b) 396 2) 2) 396 198 Take the last 3 digits and divide by 2, then divide by 2, then divide by 2

21. 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

22. 6 9 + + 5 2 + + 1 4 + = Dividing by 9 For example, take the number 924,561 • Add up the digits of the number 27 • If that number is divisible by 9, 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

23. Now You Try • 578 • 399 • 144 Sum of 5+7+8 =20 NO Sum of 3+9+9 =21 NO Are these numbers divisible by 9? Sum of 1+4+4 =9

24. Dividing by 10 • If the number ends with a 0 30 ÷ 10 = 3 340 ÷ 10 = 34 67 ÷ 10 = 6 R7 784 ÷ 10 =78 R4

25. Now You Try • 5782 • 390 • 45 Are these numbers divisible by 10?

26. Dividing by 11 • There is no special rule to help you know if a number is divisible by 11…

27. Now You Try • 99 • 88 • 121 Are these numbers divisible by 11?

28. Divisible by 1 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 REVIEW Thumbs up if you remember the rule.

29. After All… DIVISIBILITY Rules That's all Folks! Take Out Your Study Guide!!!

30. RULES FOR DIVISIBILITY #1 IF A Number Is Divisible By: 2 3 4 5 6 8 9 10 The last digit is even (0, 2, 4, 6, 8) The sum of the digits is divisible by 3 The last 2 digits are divisible by 4 The last digit is 0 or 5 It is divisible by 2 and 3 The last 3 digits are divisible by 8 The sum of the digits is divisible by 9 The last digit is 0

31. #2 IS THE NUMBER DIVISIBLE EXACTLY BY? WRITE yes (y) or no (n) REMEMBER: Show the sums for 3, and show the division for 4 and 8. 30 180 y y y y y 2) 360 2) 60 3+6 = 9 90 y y 15 2) 180 y 2) 30 45 2) 90