Discovering Divisibility Rules

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!

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

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!

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

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!

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

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!

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

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!

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

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!

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

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!

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

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

Assignment Divisibility Rules WS You can do it!