1. Divisibility Rules Outcome A6 – Develop and apply divisibility rules for 3, 4, 6, 9

2. Divisibility rule for 3 If you add the digits of a number divisible by three the sum must be divisible by three. If you add the digits of a number divisible by three the sum must be divisible by three. Example: Example: 465 → 4 + 6 + 5 = 15 465 → 4 + 6 + 5 = 15 15 → 1 + 5 = 6 15 → 1 + 5 = 6 6 ÷ 3 = 2 6 ÷ 3 = 2 Because 6 was divisible by three 465 is divisible by three Because 6 was divisible by three 465 is divisible by three

3. Divisibility rule for 4 If a number is divisible by 4 the last two digits are divisible by 4. If a number is divisible by 4 the last two digits are divisible by 4. Example: Example: 1364 → 64 ÷ 4 = 16 1364 → 64 ÷ 4 = 16 **remember this works because 100 is divisible by 4 (100 ÷ 4 = 25) that means 1300 is divisible by 4 so we only need to worry about the last two digits.

4. Divisibility rule for 6 If a number is divisible by 6 it must be divisible by both 2 and 3. If a number is divisible by 6 it must be divisible by both 2 and 3. Remember a number is divisible by two if it is even. See earlier notes for divisibility of 3. Remember a number is divisible by two if it is even. See earlier notes for divisibility of 3. Example: Example: 672 → is an even number so it is divisible by 2 672 → is an even number so it is divisible by 2 672 → 6 + 7 + 2 = 15 → 1 + 5 = 6 → 6 ÷ 3 = 2 672 → 6 + 7 + 2 = 15 → 1 + 5 = 6 → 6 ÷ 3 = 2 Because the number meets both rules it is divisible by 6. Because the number meets both rules it is divisible by 6.

5. Divisibility rule for 9 If you add the digits of a number divisible by 9 then the sum of the numbers must be divisible by 9. If you add the digits of a number divisible by 9 then the sum of the numbers must be divisible by 9. Example: Example: 576 → 5 + 7 + 6 = 18 → 18 ÷ 9 = 2 576 → 5 + 7 + 6 = 18 → 18 ÷ 9 = 2 576 is divisible by 9 576 is divisible by 9

6. Divisibility Questions.

7. 1. Is 136 divisible by 3? Explain why or why not.

8. 2. Is 244 divisible by 4. Explain why or why not.

9. 3. Is 294 divisible by 6? Explain why or why not.

10. 4. Is 5652 divisible by 9? Explain why or why not.

11. 5. Fill in the missing digit so the numbers are divisible by 9. a. 34__ b. 59__45 c. __5004

12. 6. Guess the number… The number is odd and greater than 200 but less than 401. The number is divisible by 5 and 9.

13. 7. Guess the number… The number is less than 100 and is divisible by 2, 5 and 8.

14. 8. Guess the number… The number is less than 172 but greater than 90. The number is divisible by 3, 5, and 9.

15. 9. Create your own guess the number question.

16. Divisibility Answers.

17. 1. Is 136 divisible by 3? Explain why or why not. No, because 1+3+6 = 10 and 10 is not divisible by 3. The divisibility rule for three is that if we add all the digits, the sum must be divisible by three.

18. 2. Is 244 divisible by 4. Explain why or why not. Yes, because 44 ÷ 4 = 11. The divisibility rule for 4 is that if the last two digits are divisible by four then the whole number is divisible by 4.

19. 3. Is 294 divisible by 6? Explain why or why not. Yes, because it is even and 2+9+4 = 15 and 15 ÷ 3 = 5. That means 294 meets the divisibility rule for 2 and 3 and is therefore divisible by 6.

20. 4. Is 5652 divisible by 9? Explain why or why not. Yes, because 5+6+5+2 = 18 and 18 is divisible by 9. Since the sum of the digits is divisible by 9 then the number is divisible by 9.

21. 5. Fill in the missing digit so the numbers are divisible by 9. a. 34__ = 342 b. 59__45 = 59445 c. __5004 = 95004 or 05004

22. 6. Guess the number… The number is odd and greater than 200 but less than 401. The number is divisible by 5 and 9. If the number is divisible by 5 and odd the last digit must be a 5. the three numbers must add up to a multiple of 9. Since the last digit is a 5 the first two digits must add up to 4 or 13. They can’t add up to 13 because the first digit must be either 2 or 3. If the first digit is a 2 and the last digit is a 5 then the number must be 225 (2+2+5=9) If the first digit is a 3 then it must be 3+1+5=9 so 315 So there are two answers 225 and 315

23. 7. Guess the number… The number is less than 100 and is divisible by 2, 5 and 8. Because the number is divisible by both 2 and 5 the number must end in a zero (5 must have a last digit of 5 or 0 but 5 is not even so it is not divisible by 2) so the number could be 10, 20, 30, 40, 50, 60, 70, 80, or 90 The number must also be divisible by 8 so it could be either 40 or 80 as they are both multiples of 8.

24. 8. Guess the number…The number is less than 172 but greater than 90. The number is divisible by 3, 5, and 9. We know that all numbers that are divisible by 9 are also divisible by 3 so we only have to worry about 9 and 5. We know that all numbers that are divisible by 9 are also divisible by 3 so we only have to worry about 9 and 5. From the divisibility rule for 5 we know the number must end in a 5 or 0. From the divisibility rule for 9 we know the sum of the digits must be divisible by 9. From the divisibility rule for 5 we know the number must end in a 5 or 0. From the divisibility rule for 9 we know the sum of the digits must be divisible by 9. If we guess the last digit is 0 then the first digit or first two digits must add to 9. 90 does not work because the number must be greater than 90. and the greatest number we can go to is 170 but 1+7+0 is only 8 so we do not have a factor of 9. So the last number must be 5. If we guess the last digit is 0 then the first digit or first two digits must add to 9. 90 does not work because the number must be greater than 90. and the greatest number we can go to is 170 but 1+7+0 is only 8 so we do not have a factor of 9. So the last number must be 5. If the last number is 5 then the first digit or digits must add together with 5 to equal 9. The first digit must be a 1. If the last number is 5 then the first digit or digits must add together with 5 to equal 9. The first digit must be a 1. So 1+___+5=9 the second digit must be a 3 So 1+___+5=9 the second digit must be a 3 135 is divisible by 3, 5, and 9. 135 is divisible by 3, 5, and 9.

25. 9. Create your own guess the number question.

26. Practice No Calculators allowed!! No Calculators allowed!! Textbook page 31-33 Textbook page 31-33 #1-8, 11-13, 15, 18, 19 #1-8, 11-13, 15, 18, 19