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Discovering Divisibility Rules

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**These numbers are all divisible by 2. Can you see why?**

4 18 912 636 9,720 Here’s a hint -- The ones digit is even!

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**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

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**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!

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**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

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**These numbers are all divisible by 4. Can you see why?**

16 912 720 8,224 917,532 Here’s a hint -- If the last two digits form a number divisible by 4!

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**Are these numbers divisible by 4?**

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

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**These numbers are all divisible by 5. Can you see why?**

15 280 2,475 82,470 153,645 Here’s a hint -- The ones digit is a 0 or 5!

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**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

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**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!

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**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

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**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!

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**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

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**These numbers are all divisible by 10. Can you see why?**

50 240 8,770 42,420 153,640 Here’s a hint -- The ones digit is 0!

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**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

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**Determine whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10.**

712 2, 4 1,035 3, 5, 9 32,221 none 8,340 2, 3, 4, 5, 6, 10

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Assignment Divisibility Rules WS You can do it!

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