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# Discovering

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1. Discovering Divisibility Rules

2. These numbers are all divisible by 2. Can you see why? Here’s a hint -- • 4 • 18 • 912 • 636 • 9,720 The ones digit is even!

3. A number is divisible by 2 if the ones digit is even. Are these numbers divisible by 2? 5 82 917 5,276 8,478,184 NO YES NO YES YES

4. These numbers are all divisible by 3. Can you see why? Here’s a hint – **Add up the digits of each number** • 9 • 63 • 714 • 225 • 9,720 The sum of the digits is divisible by 3!

5. A number is divisible by 3 if the sum of the digits is divisible by 3. Are these numbers divisible by 3? 7 27 824 271,360 9,265,689 NO YES NO NO YES

6. These numbers are all divisible by 4. Can you see why? Here’s a hint -- • 16 • 912 • 720 • 8,224 • 917,532 If the last two digits form a number divisible by 4!

7. A number is divisible by 4 if the last two digits form a number divisible by 4. Are these numbers divisible by 4? 15 240 1,693 4,408 12,982,540 NO YES NO YES YES

8. These numbers are all divisible by 5. Can you see why? Here’s a hint -- • 15 • 280 • 2,475 • 82,470 • 153,645 The ones digit is a 0 or 5!

9. A number is divisible by 5 if the ones digit is a 0 or 5. Are these numbers divisible by 5? 15 240 1,693 4,408 12,982,540 YES YES NO NO YES

10. These numbers are all divisible by 6. Can you see why? Here’s a hint – **Think about our other rules and what two numbers are factors of 6.** • 48 • 90 • 174 • 1,044 • 39,720 The number is divisible by both 2 and 3!

11. A number is divisible by 6 if the number is divisible by both 2 and 3. Are these numbers divisible by 6? 135 462 7,026 50,319 12,982,440 NO YES YES NO YES

12. These numbers are all divisible by 9. Can you see why? Here’s a hint – **Add up the digits of each number** • 18 • 612 • 7,443 • 81,225 • 99,720 The sum of the digits is divisible by 9!

13. A number is divisible by 9 if the sum of the digits is divisible by 9. Are these numbers divisible by 9? 72 183 1,287 189,101 12,982,440 YES NO YES NO NO

14. These numbers are all divisible by 10. Can you see why? Here’s a hint -- • 50 • 240 • 8,770 • 42,420 • 153,640 The ones digit is 0!

15. A number is divisible by 10 if the ones digit is 0. Are these numbers divisible by 10? 70 183 1,280 189,101 142,982,530 YES NO YES NO YES

16. Determine whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. 2, 4 712 3, 5, 9 1,035 none 32,221 8,340 2, 3, 4, 5, 6, 10

17. Assignment • Divisibility Rules WS You can do it!