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## Divisibility

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**Divisibility**Rules**What is Divisibility?**• Divisibility means that after dividing, there will be No remainder.**Can you tell by just looking at this**number if it is divisible by 2? by 5? by 10? by 3 ? by 9? By 6? The divisibility rules can help YOU! 356,821**Divisibility Ruleshelp you learnshortcutsto tell when a**number can be divided by another number with NO REMAINDER.**Dividing By 1**• All numbers are divisible by 1**Now You Try**• 578 • 1201 • 465 Are these numbers divisible by 1?**Dividing by 2**• All even numbers are divisible by 2 • Even numbers are numbers that • end with either 2, 4, 6, 8, or 0 18 ÷ 2 = 9 22 ÷ 2 = 11 Notice that both of these numbers are even. 21 ÷ 2 = 10 R1 NOT EVEN**Now You Try**• 458 • 1279 • 759 Not an evennumber Not an evennumber Are these numbers divisible by 2?**Dividing 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: 1 + 3 + 5 = 9 Yes, 135 is divisible by 3 because the sum of the digits is divisible by 3.**Now You Try**Sum of 6+3+9 =18 • 639 b) 56 Sum of 5+6 =11NO Are these numbers divisible by 3? Sum of 7+3+8 =18 c) 738**Dividing by 4**• If the last 2 digits together are divisible by 4 • or take your number, divide it by 2. Then divide that answer by 2, and if you get an EVEN NUMBER then it is divisible by 4 Example 384 21 4) 84 180 EVEN 90 EVEN Example 360 2) 2) 360 180**Now You Try**21 • 584 • 261 4) 84 Are these numbers divisible by 4? 15 r1 NO 4) 61 Take the last 2 digits and divide by 4**Dividing by 5**• If the number ends in 5 or 0 • 25 ÷ 5 = 5 • 23 ÷ 5 = 4 R3 NO**Now You Try**• 554 • 6890 • 345 Are these numbers divisible by 5?**Dividing by 6**• If the number is divisible by 2, • AND . . . • If the number is divisible by 3**Now You Try**• 897 • 258 • 630 No it is not EVEN Are these numbers divisible by 6? EVEN, Sum of 2+5+8 =15 EVEN, Sum of 6+3+0 =9**Dividing by 7**• There is no special rule to help you know if a number is divisible by 7…**Now You Try**• 500 • 49 • 2100 Are these numbers divisible by 7?**Dividing by 8**• If the last three digits are divisible by 8 • If the number is divisible by 2, • then by 2 again, and then by 2 again • So what type of number does it have to be? • A number that has been cubed.**Now You Try**284 Even 142 Even 71 • 568 2) 2) 2) 568 284 142 Are these numbers divisible by 8? 198 Even 99 Odd NO b) 396 2) 2) 396 198 Take the last 3 digits and divide by 2, then divide by 2, then divide by 2**Dividing by 9**• Similar to dividing by 3 • Add up digits • If that number is divisible by 9 then your number is divisible by 9**6**9 + + 5 2 + + 1 4 + = Dividing by 9 For example, take the number 924,561 • Add up the digits of the number 27 • If that number is divisible by 9, then the original number is Is 27 divisible by 9? • If your sum is still a big number, continue to add the digits 2 + 7 = 9**Now You Try**• 578 • 399 • 144 Sum of 5+7+8 =20 NO Sum of 3+9+9 =21 NO Are these numbers divisible by 9? Sum of 1+4+4 =9**Dividing by 10**• If the number ends with a 0 30 ÷ 10 = 3 340 ÷ 10 = 34 67 ÷ 10 = 6 R7 784 ÷ 10 =78 R4**Now You Try**• 5782 • 390 • 45 Are these numbers divisible by 10?**Dividing by 11**• There is no special rule to help you know if a number is divisible by 11…**Now You Try**• 99 • 88 • 121 Are these numbers divisible by 11?**Divisible by 1**Divisible by 2 Divisible by 3 Divisible by 4 Divisible by 5 Divisible by 6 Divisible by 7 Divisible by 8 Divisible by 9 Divisible by 10 Divisible by 11 REVIEW Thumbs up if you remember the rule.**After All… DIVISIBILITY Rules**That's all Folks! Take Out Your Study Guide!!!**RULES FOR DIVISIBILITY**#1 IF A Number Is Divisible By: 2 3 4 5 6 8 9 10 The last digit is even (0, 2, 4, 6, 8) The sum of the digits is divisible by 3 The last 2 digits are divisible by 4 The last digit is 0 or 5 It is divisible by 2 and 3 The last 3 digits are divisible by 8 The sum of the digits is divisible by 9 The last digit is 0**#2**IS THE NUMBER DIVISIBLE EXACTLY BY? WRITE yes (y) or no (n) REMEMBER: Show the sums for 3, and show the division for 4 and 8. 30 180 y y y y y 2) 360 2) 60 3+6 = 9 90 y y 15 2) 180 y 2) 30 45 2) 90