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Divisibility Rules!

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What is Divisibility? Divisibility means that after dividing, there will be no remainders. The divisor can evenly divide into the dividend.

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**356,821 The divisibility rules can help you!**

Can you tell by just looking at this number if it is divisible by 2? by 3? by 4? by 5? by 6 ? by 9? By 10? The divisibility rules can help you!

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Divisibility rules help you learn shortcuts to tell when a number can be divided by another number without any remainders.

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**Divisibility by 2 18 ÷ 2 = 9 A number is divisible by 2**

if the number is even. 18 ÷ 2 = 9 22 ÷ 2 = 11 (18 and 22: Notice that both of these dividends are even.) 21 ÷ 2 = 10 R1 (21: not an even number.)

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**Are these numbers divisible by 2?**

Now You Try Are these numbers divisible by 2? 79,458 1,279 6,249 51,553 19,050 35,792

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Divisibility 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: = 9 Yes, 135 is divisible by 3 because the sum of the digits is divisible by 3.

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**For example, take the number 738**

Dividing by 3 For example, take the number 738 Add up the digits of the number 7 + 3 8 = 18 Is 18 divisible by 3? If that number is divisible by 3, then the original number is Oh yeah! If your sum is still a big number, continue to add the digits 1 + 8 = 9 Is 9 divisible by 3?

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**Are these numbers divisible by 3?**

Now You Try Are these numbers divisible by 3? 639 56 86 360 468 2,511

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**If the last 2 digits together are divisible by 4**

Dividing by 4 If the last 2 digits together are divisible by 4 Example: 72,624 Is 24 divisible by 4? Great scott

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**Are these numbers divisible by 4?**

Now You Try Are these numbers divisible by 4? 97,584 123,261 48,156 53,920 25,767 13,224

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Divisibility by 5 A number is divisible by 5 if it ends in 0 or 5. 25 ÷ 5 = 5 23 ÷ 5 = 4 R3

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**Are these numbers divisible by 5?**

Now You Try Are these numbers divisible by 5? 198,554 6,890 31,345 68,902 371,845 20,001

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**Divisibility by 6 A number is divisible by 6**

if it is divisible by both 2 AND 3. Is 42 divisible by 6? Think: Is 42 divisible by 2? Is 42 divisible by 3? Is 51 divisible by 6? Hint: Is it an even number?

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**Are these numbers divisible by 6?**

Now You Try Are these numbers divisible by 6? 897 258 630 345 84 8,235

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Divisibility by A number is divisible by 9 if the sum of its digits is divisible by 9. 369 is divisible by 9 because =18 1 + 8 = 9 and 9 is divisible by 9.

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**Dividing by 9 Add up the digits of the number 27 9 + 2 4 6 5 1 =**

For example, take the number 924,561 Add up the digits of the number 27 9 + 2 4 6 5 1 = Is 27 divisible by 9? If that number is divisible by 3, then the original number is Oh yeah! If your sum is still a big number, continue to add the digits 2 + 7 = 9 Is 9 divisible by 9?

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**Are these numbers divisible by 9?**

Now You Try Are these numbers divisible by 9? 55,578 22,398 91,548 17,903 32,490 83,402

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**Divisibility by A number is divisible by 10 if it ends in 0.**

30 ÷ 10 = 3 340 ÷ 10 = 34 67 ÷ 10 = 6 R7 784 ÷ 10 =78 R4

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**Are these numbers divisible by 10?**

Now You Try Are these numbers divisible by 10? 24,578 39,800 48,003 19,030 490,870 65,432

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Is it divisible by: 2 3 4 5 6 9 10 444,555,448 26,350 74,673,042 61,616,168 732,510 9,623,205

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Is it divisible by: 2 3 4 5 6 9 10 123,456,789 58,468,240 52,301,042 246,813,579 135,790,135 813,423,700

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**After all, divisibility rules!**

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THE END

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