Name ______Divisibility

A number is divisible by another number if it is a true multiple of the other number (or if the division problem does not have a remainder. 24 is divisible by 3 because 24 ÷ 3 = 8 with no remainder. 25 is not divisible by 3 because it would have a remainder of 1! This first section of this booklet will help you to learn the divisibility rules that you will need and use every day. The numbers are all less than 169 because using the Fraction Actions method, you will never end up with numbers greater than 169 that are not already finished numbers. The last section of the book will help you with a few rules that you will need to know for NC EOG testing purposes. Divisibility Rules Divisibility Rule for 2 When the last digit in a number is 0, 2, 4, 6, or 8, the number is divisible by 2 Divisibility Rule for 5 When the last digit in a number is 0 or 5, the number is divisible by 5 Divisibility Rule for 3 When the sum of the digits is a multiple of 3, the number is divisible by 3 Divisibility Rule for 7 Double the last digit in a number and subtract it from the rest of the number. If the result is a known multiple of 7, then the number is divisible by 7. If the result is not known, repeat the rule with the new number! Divisibility Rule for 11 When the sum of the odd digits is equal to (or 11 more than) the sum of the even digits, the number is divisible by 11 Divisibility Rule for 13 Nine times the last digit in a number and subtract it from the rest of the number. If the result is a known multiple of 13, then the number is divisible by 13. If the result is not known, repeat the rule with the new number! Divisibility Rule for 4 When the last 2 digits in a number are a multiple of 4, the number is divisible by 4 Divisibility Rule for 6 When a number is divisible by 2 and 3, the number is divisible by 6 Divisibility Rule for 9 When the sum of the digits is a multiple of 9, the number is divisible by 9 Divisibility Rule for 10 When the last digit in a number is 0, the number is divisible by 10

© 2009 – Norm Mitchell (Math6.org) – All Rights Reserved Freely reproducible for “non-profit” educational purposes – visit http://www.math6.org/legal.htm for more details concerning “non-profit”. Divisibility (2 and 5)

Lesson Box Models

The divisibility rule for 2 and 5 ask you to look at the 2, 5 80 last digit of the number. 80 ends with 0. According to the rules, numbers that If the last digit is 0, 2, 4, 6, or 8 the number is divisible end with 0 are divisible by 2 and 5. by 2.

If the last digit is 0 or 5, the number is divisible by 5. 2 158

158 ends with 8. 8 is part of the 2 rule.

Ø 151 151 ends with 1. 1 is not part of either rule, so 151 is not divisible by 2 or 5.

5 215 215 ends with 5. Twenty-five is divisible by 5!

Apply the divisibility rules for 2 and 5. If the number is divisible by 2 or 5, write which ever answer is true. You do not need to write both answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the number is not divisible by these rules, enter Ø.

______160 ______145 ______107 ______37 ______41

______80 ______136 ______115 ______20 ______156

______158 ______133 ______120 ______137 ______59

______151 ______124 ______35 ______105 ______34

______76 ______78 ______141 ______24 ______112

______25 ______106 ______159 ______23 ______162

______108 ______36 ______44 ______68 ______61

______66 ______103 ______111 ______167 ______100

______87 ______73 ______157 ______67 ______96

______72 ______130 ______46 ______54 ______30

______29 ______154 ______74 ______89 ______99

[use Key 1 to check your answers] Divisibility (3)

Lesson Box Models

The divisibility rule for 3 asks you to find the sum of 3 138 the digits. 1 + 8 = 9 (or 1 + 3 + 8 = 12) If the sum of the digits is a multiple of 3, then the number is divisible by 3. Ø 58

257 5 + 8 = 13 2 + 5 + 7 = 14. 14 is not a multiple of 3. 257 is not divisible by 3. 3 126

342 1 + 2 = 3 (or 1 + 2 + 6 = 9) 3 + 4 + 2 = 9. 9 is a multiple of 3. 342 is divisible by 3. Ø 101

To cast out 3’s don’t add any 3, 6 or 9’s. 1 + 1 = 2 342 … 4 + 2 = 6 268 … 2 + 8 = 10 692 … 2 = 2

Apply the divisibility rule for 3. If the number is divisible by 3, write 3. If the number is not divisible by 3, enter Ø.

______47 ______164 ______54 ______156 ______108

______70 ______68 ______137 ______55 ______117

______122 ______77 ______92 ______107 ______106

______140 ______61 ______83 ______87 ______31

______169 ______148 ______141 ______78 ______41

______51 ______145 ______56 ______96 ______74

______111 ______46 ______90 ______155 ______19

______60 ______64 ______44 ______72 ______124

______86 ______81 ______75 ______167 ______36

______100 ______131 ______159 ______134 ______95

______38 ______119 ______166 ______69 ______59

______14 ______26 ______50 ______40 ______29

[use Key 2 to check your answers] Divisibility Drills 2, 3 and 5

Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the number is not divisible by these rules, enter Ø.

______103 ______75 ______65 ______30 ______139

______24 ______112 ______28 ______105 ______123

______53 ______143 ______64 ______26 ______136

______49 ______90 ______164 ______140 ______96

______50 ______152 ______111 ______104 ______125

______31 ______81 ______145 ______71 ______113

______169 ______107 ______95 ______131 ______129

______19 ______165 ______149 ______29 ______124

______36 ______127 ______137 ______84 ______109

______141 ______32 ______63 ______100 ______14

[use Key 3 to check your answers]

Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the number is not divisible by these rules, enter Ø.

______55 ______48 ______98 ______40 ______83

______119 ______155 ______130 ______151 ______157

______51 ______106 ______116 ______135 ______27

______17 ______70 ______25 ______117 ______42

______120 ______156 ______160 ______62 ______34

______101 ______41 ______133 ______121 ______72

______153 ______146 ______159 ______148 ______45

______44 ______134 ______167 ______122 ______79

______162 ______161 ______67 ______168 ______126

______154 ______12 ______110 ______85 ______23 [use Key 4 to check your answers] Divisibility (7)

Lesson Box Models

• Double the last digit in a number and subtract it from the rest of the number. Ø 138 • If the result is a known multiple of 7, then the number is divisible by 7. 8*2 = 16 ; 16-13 = 3 ; 138 is not divisible by 7 • If the result is not known, repeat the rule with

the new number! 7 168 257 8*2 = 16 ; 16-16 = 0 ; 168 is divisible by 7 7 * 2 = 14.

25 – 14 = 11.

257 is not divisible by 7. 7 133

343 3*2 = 6 ; 13-6 = 7 ; 133 is divisible by 7 3 * 2 = 6.

34 – 6 = 28.

343 is divisible by 7. Ø 101

49 1*2 = 2 ; 10-2 = 8 ; 101 is not divisible by 7 9 * 2 = 18.

18 – 4 = 14.

49 is divisible by 7. (notice you can subtract the first digits from the doubled last if you need to!)

Apply the divisibility rule for 7. If the number is divisible by 7, write 7. If the number is not divisible by 7, enter Ø.

______46 ______117 ______139 ______66 ______70

______55 ______161 ______140 ______31 ______69

______111 ______153 ______35 ______63 ______119

______49 ______132 ______105 ______13 ______78

______141 ______28 ______93 ______110 ______130

______156 ______88 ______121 ______143 ______95

______15 ______155 ______54 ______21 ______136

______60 ______166 ______72 ______23 ______123

______133 ______59 ______167 ______17 ______107

______92 ______160 ______45 ______168 ______145

______30 ______102 ______43 ______68 ______41

______152 ______142 ______83 ______149 ______124

[use Key 5 to check your answers] Divisibility Drills 2, 3, 5, and 7

Apply the divisibility rules for 2, 3, 5 and 7. If the number is divisible by 2, 3, 5 or 7, write which ever answer is true. You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the number is not divisible by these rules, enter Ø.

______163 ______95 ______128 ______81 ______18

______142 ______29 ______38 ______149 ______40

______28 ______69 ______101 ______156 ______117

______80 ______31 ______162 ______90 ______16

______129 ______160 ______34 ______77 ______67

______136 ______97 ______58 ______167 ______105

______124 ______32 ______139 ______126 ______144

______141 ______146 ______88 ______140 ______111

______92 ______169 ______78 ______19 ______15

______65 ______107 ______96 ______123 ______89 Key 6 [use to check your answers]

Apply the divisibility rules for 2, 3, 5 and 7. If the number is divisible by 2, 3, 5 or 7, write which ever answer is true. You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the number is not divisible by these rules, enter Ø.

______147 ______35 ______164 ______47 ______82

______158 ______132 ______93 ______118 ______110

______33 ______76 ______113 ______49 ______133

______68 ______52 ______43 ______22 ______57

______75 ______21 ______119 ______154 ______70

______64 ______166 ______168 ______42 ______27

______72 ______130 ______51 ______103 ______79

______85 ______24 ______45 ______39 ______100

______104 ______62 ______120 ______56 ______63

______61 ______134 ______137 ______159 ______145 [use Key 7 to check your answers] Divisibility (11)

Lesson Box Models

When the sum of the odd digits is equal to (or 11 more than) the sum of the even digits, the number is divisible 11 264 by 11. 2 + 4 = 6 257 7 + 2 ≠ 5. Ø 235 257 is not divisible by 11. 2 + 5 ≠ 3 2574 2 + 7 = 5 + 4. 257 is divisible by 11. 11 220

346 2 + 0 = 2 3 + 6 ≠ 4. 346 is not by 11. Ø 212 209 2 + 9 = 0 (+ 11more) 2 + 2 ≠ 1 209 is divisible by 11. 11 968

9 + 8 = 6 (+ 11 more)

Apply the divisibility rule for 11. If the number is divisible by 11, write 11. If the number is not divisible by 11, enter Ø.

______151 ______110 ______153 ______132 ______119

______129 ______154 ______99 ______141 ______147

______166 ______165 ______113 ______135 ______112

______143 ______162 ______109 ______120 ______156

______117 ______155 ______159 ______104 ______146

______107 ______158 ______106 ______163 ______126

______149 ______139 ______123 ______150 ______103

______160 ______124 ______142 ______128 ______131

______118 ______114 ______102 ______133 ______164

______167 ______148 ______157 ______130 ______121

______125 ______134 ______101 ______100 ______168

[use Key 8 to check your answers] Divisibility Drills 2, 3, 5, 7, and 11

Apply the divisibility rules for 2, 3, 5, 7, and 11. If the number is divisible by 2, 3, 5, 7, and 11, write which ever answer is true. You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the number is not divisible by these rules, enter Ø.

______27 ______159 ______43 ______126 ______143

______90 ______53 ______84 ______110 ______51

______57 ______40 ______45 ______46 ______92

______47 ______100 ______21 ______96 ______131

______42 ______129 ______142 ______140 ______26

______125 ______75 ______101 ______78 ______83

______73 ______156 ______56 ______97 ______34

______161 ______145 ______86 ______150 ______49

______31 ______128 ______98 ______106 ______16

______15 ______99 ______164 ______79 ______112 Key 9 [use to check your answers]

Apply the divisibility rules for 2, 3, 5, 7, and 11. If the number is divisible by 2, 3, 5, 7, and 11, write which ever answer is true. You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the number is not divisible by these rules, enter Ø.

______28 ______146 ______111 ______12 ______103

______148 ______74 ______141 ______13 ______50

______154 ______20 ______58 ______63 ______167

______162 ______94 ______127 ______29 ______144

______155 ______70 ______82 ______71 ______19

______160 ______118 ______30 ______152 ______69

______32 ______107 ______139 ______135 ______85

______59 ______113 ______48 ______41 ______72

______121 ______149 ______157 ______33 ______80

______60 ______52 ______64 ______24 ______67 [use Key 10 to check your answers] Divisibility Drills – Proof of Mastery – No Errors Allowed!

Apply the divisibility rules for 2, 3, 5, 7, and 11. If the number is divisible by 2, 3, 5, 7, and 11, write which ever answer is true. You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the number is not divisible by these rules, enter Ø.

______129 ______36 ______105 ______99 ______112

______72 ______47 ______34 ______87 ______46

______120 ______157 ______146 ______17 ______135

______26 ______92 ______149 ______31 ______83

______23 ______168 ______73 ______16 ______123

______33 ______56 ______59 ______169 ______49

______141 ______150 ______158 ______122 ______138

______96 ______152 ______153 ______42 ______35

______103 ______156 ______25 ______82 ______79

______154 ______107 ______54 ______130 ______65 Key 11 [use to check your answers]

Apply the divisibility rules for 2, 3, 5, 7, and 11. If the number is divisible by 2, 3, 5, 7, and 11, write which ever answer is true. You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the number is not divisible by these rules, enter Ø.

______139 ______164 ______12 ______32 ______144

______85 ______80 ______45 ______163 ______81

______50 ______159 ______110 ______161 ______102

______95 ______69 ______62 ______75 ______53

______101 ______70 ______148 ______67 ______115

______84 ______29 ______37 ______44 ______30

______21 ______116 ______60 ______143 ______142

______113 ______43 ______28 ______145 ______27

______108 ______63 ______137 ______78 ______40

______134 ______98 ______74 ______89 ______88 [use Key 12 to check your answers] Congratulations!

If you made 0 errors, you have mastered the rules you will use to find prime and composite numbers and never be puzzled when doing prime factoring problems. If you need more practice, you can visit the divisibility rules page @ Math6.org and keep your skills sharp. Practice the rules that give you the butterflies, not the ones you are good at! You may also print the problems only version of this workbook so that you can drill yourself to greater mastery.

To tell whether a number that is less than 169 is prime or composite, simply check it for divisibility by 2, 3, 5, 7, and 11. As soon as it passes one of those rules, the number is composite. If it fails all of the rules, the number is prime! You could add the 13 rule so that you could go past 169, but you will need that rule so rarely that most teachers don’t ask you to go there. If you want help with the 13 rule, Math6.org offers help.

Using these rules to know the divisor for a factor tree will help you to quickly and efficiently find the prime factors of any number. Prime Factoring easy numbers is the foundation of the Fraction Actions method as taught @ Math6.org. By using the Fraction Actions method, all fraction problems become very similar and you will find that fraction problems become easy. To learn more about prime factoring or the Fraction Actions method, visit the Fraction Actions page @ Math6.org.

Since most fractions methods require you to know all of the factors of a number, there are a few more rules to master. Most tests will want to know all of the rules. We still need to work on and master the following rules to declare ourselves a Divisibility Rules Master. Divisibility Rules Divisibility Rule for 4 When the last 2 digits in a number are a multiple of 4, the number is divisible by 4 Divisibility Rule for 6 When a number is divisible by 2 and 3, the number is divisible by 6 Divisibility Rule for 9 When the sum of the digits is a multiple of 9, the number is divisible by 9 Divisibility Rule for 10 When the last digit in a number is 0, the number is divisible by 10

The following sets of drills will ask you to list all of the numbers that the given number is divisible by. You will need to master this skill for testing purposes and to make fractions easier if you choose to learn a method for fraction computations other than the Fraction Actions method.

Divisibility (4)

Lesson Box Models

When the last 2 digits in a number are a multiple of 4, the number is divisible by 4. (if the 10’s digit is even, 4 276 the final digit will be 4 or 8. If the 10’s digit is odd, the final digit will be 0, 2 or 6. 76 is a multiple of 4.

338 and 2738 4 248 38 is not a multiple of 4. 338 and 2738 are not divisible by 4. 48 is a multiple of 4.

272 and 3172 72 is a multiple of 4. Ø 170 272 and 3172 are divisible by 4. 70 is not a multiple of 4. 285 and 47285 85 is not a multiple of 4. 285 and 47285 are not divisible by 4. Ø 455

312 and 916312 55 is not a multiple of 4. 12 is a multiple of 4. 312 and 916312 are divisible by 4. 4 392

92 is a multiple of 4.

Apply the divisibility rule for 4. If the number is divisible by 4, write 4. If the number is not divisible by 4, enter Ø.

______32 ______127 ______90 ______134 ______143

______62 ______56 ______54 ______166 ______114

______118 ______34 ______100 ______98 ______144

______66 ______48 ______28 ______149 ______40

______128 ______124 ______131 ______52 ______60

______88 ______94 ______38 ______44 ______168

______132 ______136 ______165 ______108 ______104

______112 ______130 ______78 ______115 ______92

______122 ______106 ______80 ______160 ______158

______86 ______123 ______36 ______142 ______58

______148 ______74 ______146 ______167 ______162

______135 ______138 ______30 ______76 ______26

[use Key 13 to check your answers] Divisibility Drills 2, 3, 4, 5, 7, and 11

Tell whether each number is divisible by 2, 3, 4, 5, 7, and 11. If the number is not divisible by these rules, enter Ø.

______56 ______92 ______150

______28 ______87 ______65

______49 ______25 ______147

______38 ______31 ______36

______163 ______57 ______18

______82 ______122 ______128

______45 ______145 ______62

______71 ______135 ______35

______168 ______160 ______126

______16 ______23 ______79

______111 ______12 ______14

______88 ______32 ______151 [use Key 14 to check your answers]

Tell whether each number is divisible by 2, 3, 4, 5, 7, and 11. If the number is not divisible by these rules, enter Ø.

______72 ______78 ______63

______85 ______149 ______99

______100 ______69 ______70

______166 ______53 ______138

______134 ______96 ______105

______156 ______52 ______86

______61 ______64 ______121

______47 ______131 ______80

______157 ______127 ______169

______117 ______29 ______165

______13 ______120 ______144

______59 ______123 ______162 [use Key 15 to check your answers] Divisibility (6)

Lesson Box Models

If a number is divisibly by both 2 and 3, the number is also divisible by 6! 6 144

312 4 works for 2. 1 + 4 + 4 = 9 312 is divisible by 2. 1 + 2 = 3 Ø 328 312 is divisible by 6. 4 works for 2. 2 + 8 = 10 320 320 is divisible by 2. 2 is not a multiple of 3 Ø 260 320 is not divisible by 6. 0 works for 2. 2 + 6 = 8 297 297 is not divisible by 2. 297 is not divisible by 6. Ø 275

228 5 does not work for 2. 228 is divisible by 2. 2 + 8 + 2 = 12 6 336 228 is divisible by 6. 6 works for 2. I tossed out all of the numbers!

Apply the divisibility rule for 6. If the number is divisible by 6, write 6. If the number is not divisible by 6, enter Ø.

______66 ______154 ______105 ______96 ______135

______158 ______58 ______56 ______22 ______102

______86 ______32 ______150 ______117 ______126

______49 ______60 ______64 ______144 ______20

______90 ______85 ______145 ______118 ______148

______155 ______40 ______87 ______130 ______78

______92 ______106 ______24 ______128 ______162

______38 ______44 ______62 ______26 ______69

______12 ______114 ______100 ______88 ______54

______115 ______104 ______142 ______138 ______140

______18 ______27 ______111 ______15 ______46

______134 ______89 ______136 ______30 ______120

[use Key 16 to check your answers] Divisibility Drills 2, 3, 4, 5, 6, 7, and 11

Tell whether each number is divisible by 2, 3, 4, 5, 6, 7, and 11. If the number is not divisible by these rules, enter Ø.

______153 ______149 ______92

______31 ______55 ______28

______64 ______147 ______106

______24 ______129 ______32

______83 ______75 ______81

______36 ______35 ______102

______12 ______60 ______101

______19 ______72 ______168

______21 ______51 ______115

______139 ______16 ______112

______107 ______57 ______122

______47 ______30 ______56 [use Key 17 to check your answers]

Tell whether each number is divisible by 2, 3, 4, 5, 6, 7, and 11. If the number is not divisible by these rules, enter Ø.

______71 ______114 ______66

______134 ______159 ______63

______23 ______152 ______111

______90 ______131 ______165

______155 ______109 ______22

______138 ______87 ______95

______49 ______135 ______13

______86 ______119 ______27

______69 ______97 ______125

______150 ______74 ______85

______158 ______15 ______117

______116 ______126 ______166 [use Key 18 to check your answers] Divisibility (9)

Lesson Box Models

The divisibility rule for 9 asks you to find the sum of Ø 581 the digits. If the sum of the digits is a multiple of 9, then the number is divisible by 9. 5 + 8 + 1 = 14

297 9 657 2 + 9 + 7 = 18. 18 is a multiple of 9. 6 + 5 + 7 = 18 297 is divisible by 9.

342 Ø 921 3 + 4 + 2 = 9. 9 is a multiple of 9. 2 + 1 = 3 (or 9 + 2 + 1 = 12) 342 is divisible by 9.

To cast out 9’s don’t add any 9’s. 9 369 954 … 5 + 4 = 9 298 … 2 + 8 = 10 3 + 6 = 9 (or 3 + 6 + 9 = 18) 692 … 2 + 6 = 8 9 783

7 + 8 + 3 = 18

Apply the divisibility rule for 9. If the number is divisible by 9, write 9. If the number is not divisible by 9, enter Ø.

______129 ______110 ______166 ______104 ______572

______117 ______288 ______324 ______127 ______664

______254 ______290 ______210 ______228 ______448

______206 ______256 ______298 ______153 ______208

______143 ______226 ______270 ______322 ______456

______144 ______162 ______125 ______268 ______306

______208 ______252 ______234 ______142 ______644

______111 ______113 ______126 ______108 ______536

______157 ______216 ______286 ______161 ______284

______222 ______105 ______332 ______167 ______216

______103 ______116 ______135 ______134 ______334

______114 ______260 ______224 ______468 ______592

[use Key 19 to check your answers] Divisibility Drills 2, 3, 4, 5, 6, 7, 9, 10 and 11 (all rules)

Tell whether each number is divisible by 2, 3, 4, 5, 6, 7, 9, 10 and 11. If not enter Ø.

______134 ______111 ______79

______154 ______68 ______109

______108 ______133 ______105

______49 ______63 ______48

______82 ______17 ______120

______31 ______90 ______76

______45 ______64 ______119

______15 ______88 ______59

______62 ______158 ______13

______131 ______104 ______20

______42 ______47 ______95

______84 ______148 ______92 [use Key 20 to check your answers]

Tell whether each number is divisible by 2, 3, 4, 5, 6, 7, 9, 10 and 11. If not enter Ø.

______37 ______166 ______101

______145 ______124 ______167

______152 ______116 ______89

______22 ______149 ______71

______132 ______107 ______159

______24 ______141 ______163

______23 ______87 ______53

______99 ______150 ______29

______126 ______85 ______106

______16 ______32 ______103

______61 ______83 ______143

______144 ______50 ______78 [use Key 21 to check your answers] Apply the divisibility rules for 2 and 5. If the number is divisible by 2 or 5, write which ever answer is true. You do not need to write both answers. (example: 110 is divisibleKey by 1both 2 and 5, you may answer 2) If the number is not Any one answer from the list is correct! divisible by these rules, enter Ø.

2,5 5 Ø Ø Ø

2,5 2 5 2 2

2 Ø 2,5 Ø Ø

Ø 2 5 5 2

2 2 Ø 2 2

5 2 Ø Ø 2

2 2 2 2 Ø

2 Ø Ø Ø 2,5

Ø Ø Ø Ø 2

2 2,5 2 2 2,5

Ø 2 2 Ø Ø

3 Apply the divisibility rule for . If the number is divisibleKey by 2 3, write 3. If the number is not divisible by 3, enter Ø.

Ø Ø 3 3 3

Ø Ø Ø Ø 3

Ø Ø Ø Ø Ø

Ø Ø Ø 3 Ø

Ø Ø 3 3 Ø

3 Ø Ø 3 Ø

3 Ø 3 Ø Ø

3 Ø Ø 3 Ø

Ø 3 3 Ø 3

Ø Ø 3 Ø Ø

Ø Ø Ø 3 Ø

Ø Ø Ø Ø Ø Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. You do not need to write all of the answers. (example: 110Key is 3 divisible by both 2 and 5, you may answer 2) If the Any one answer from the list is correct! number is not divisible by these rules, enter Ø.

Ø 3, 5 5 2, 3 Ø

2, 3 2 3 3

Ø Ø 2 2 2

Ø 2, 3, 5 2 2 2, 3

2, 5 2 3 2 5

Ø 3 5 Ø Ø

Ø Ø 5 Ø 3

Ø 3, 5 Ø Ø 2

2, 3, 5 Ø Ø 2, 3 Ø

3 2 3 2, 5 2

Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. Key 4 You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the Any one answer from the list is correct! number is not divisible by these rules, enter Ø.

5 2, 3 2 2, 5 Ø

Ø 5 2, 5 Ø Ø

3 2 2 3, 5 3

Ø 2, 5 5 3 2, 3

2, 3, 5 2, 3 2, 5 2 2

Ø Ø Ø Ø 2, 3

3 2 3 2 3, 5

2 2 Ø 2 Ø

2, 3 Ø Ø 2, 3 2, 3

2 2, 3 2, 5 5 Ø Apply the divisibility rule for 7. If the number is divisible by 7, write 7. If the number is not divisible by 7, enter Ø. Key 5

Ø Ø Ø Ø 7

Ø 7 7 Ø Ø

Ø Ø 7 7 7

7 Ø 7 Ø Ø

Ø 7 Ø Ø Ø

Ø Ø Ø Ø Ø

Ø Ø Ø 7 Ø

Ø Ø Ø Ø Ø

7 Ø Ø Ø Ø

Ø Ø Ø 7 Ø

Ø Ø Ø Ø Ø

Ø Ø Ø Ø Ø

Apply the divisibility rule for 11. If the number is divisible by 11, write 11. If the number is not divisible by 11, Key 8 enter Ø.

Ø 11 Ø 11 Ø

Ø 11 11 Ø Ø

Ø 11 Ø Ø Ø

11 Ø Ø Ø Ø

Ø Ø Ø Ø Ø

Ø Ø Ø Ø Ø

Ø Ø Ø Ø Ø

Ø Ø Ø Ø Ø

Ø Ø Ø Ø Ø

Ø Ø Ø Ø 11

Ø Ø Ø Ø Ø Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. You do not need to write all of the answers. (example: 110Key is 6 divisible by both 2 and 5, you may answer 2) If the Any one answer from the list is correct! number is not divisible by these rules, enter Ø.

Ø 5 2 3 2, 3

2 Ø 2 Ø 2, 5

2,7 3 Ø 2, 3 3

2, 5 Ø 2, 3 2, 3, 5 2

3 2, 5 2 7 Ø

2 Ø 2 Ø 3, 5, 7

2 2 Ø 2, 3, 7 2, 3

3 2 2 2, 5, 7 3

2 Ø 2, 3 Ø 3, 5

5 Ø 2, 3 3 Ø

Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. Key 7 You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the Any one answer from the list is correct! number is not divisible by these rules, enter Ø.

3, 7 5, 7 2 Ø 2

2 2, 3 3 2 2, 5

3 2 Ø 7 7

2 2 Ø 2 3

3, 5 3, 7 7 2, 7 2, 5, 7

2 2 2, 3, 7 2, 3, 7 3

2, 3 2, 5 3 Ø Ø

5 2, 3 3, 5 3 2, 5

2 2 2, 3, 5 2, 7 3, 7

Ø 2 Ø 3 5 Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. You do not need to write all of the answers. (example: 110Key is 9 divisible by both 2 and 5, you may answer 2) If the Any one answer from the list is correct! number is not divisible by these rules, enter Ø.

3 3 Ø 2, 3, 7 11

2, 3, 5 Ø 2, 3, 7 2, 5, 11 3

3 2, 5 3, 5 2 2

Ø 2, 5 3, 7 2, 3 Ø

2, 3, 7 3 2 2, 5, 7 2

5 3, 5 Ø 2, 3 Ø

Ø 2, 3 2, 7 Ø 2

7 5 2 2, 3, 5 7

Ø 2 2, 7 2 2

3, 5 3, 11 2 Ø 2, 7

Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. Key 10 You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the Any one answer from the list is correct! number is not divisible by these rules, enter Ø.

2, 7 2 3 2, 3 Ø

2 2 3 Ø 2, 5

2, 7 2, 5 2 3, 7 Ø

2, 3 2 Ø Ø 2, 3

5 2, 5, 7 2 Ø Ø

2, 5 2 2, 3, 5 2 3

2 Ø Ø 3, 5 5

Ø Ø 2, 3 Ø 2, 3

11 Ø Ø 3, 11 2, 5

2, 3, 5 2 2 2, 3 Ø Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. You do not need to write all of the answers. (example: 110Key is 11 divisible by both 2 and 5, you may answer 2) If the Any one answer from the list is correct! number is not divisible by these rules, enter Ø.

3 2, 3 3, 5, 7 3, 11 2, 7

2, 3 Ø 2 3 2

2, 3, 5 Ø 2 Ø 3, 5

2 2, Ø Ø Ø

Ø 2, 3, 7 Ø 2, 3

3, 11 2, 7 Ø Ø 7

3 2, 3, 5 2 2 2, 3

2, 3 2 3 2, 3, 7 5, 7

Ø 2, 3 5 2 Ø

2, 7, 11 Ø 2, 3 2, 5 5

Apply the divisibility rules for 2, 3 and 5. If the number is divisible by 2, 3 or 5, write which ever answer is true. Key 12 You do not need to write all of the answers. (example: 110 is divisible by both 2 and 5, you may answer 2) If the Any one answer from the list is correct! number is not divisible by these rules, enter Ø.

Ø 2 2, 3 2 2, 3

5 2, 5 3, 5 Ø 3

2, 5 3 2, 5, 11 7 2, 3

5 3 2 3, 5 Ø

Ø 2, 5, 7 2 Ø 5

2, 3, 7 Ø Ø 2, 11 2, 3, 5

3, 7 2 2, 3, 5 11 2

Ø Ø 2, 7 5 3,

2, 3 3, 7 Ø 2, 3 2, 5

2 2, 7 2 Ø 2, 11 Apply the divisibility rule for 7. If the number is divisible by 7, write 7. If the number is not divisible by 7, enter Ø. Key 13

4 Ø Ø Ø Ø

Ø 4 Ø Ø Ø

Ø Ø 4 Ø 4

Ø 4 4 Ø 4

4 4 Ø 4 4

4 Ø Ø 4 4

4 4 Ø 4 4

4 Ø Ø Ø 4

Ø Ø 4 4 Ø

Ø Ø 4 Ø Ø

4 Ø Ø Ø Ø

Ø Ø Ø 4 Ø

Apply the divisibility rule for 6. If the number is divisible by 6, write 6. If the number is not divisible by 6, enter Ø. Key 16

6 Ø Ø 6 Ø

Ø Ø Ø Ø 6

Ø Ø 6 Ø 6

Ø 6 Ø 6 Ø

6 Ø Ø Ø Ø

Ø Ø Ø Ø 6

Ø Ø 6 Ø 6

Ø Ø Ø Ø Ø

6 6 Ø Ø 6

Ø Ø Ø 6 Ø

6 Ø Ø Ø Ø

Ø Ø Ø 6 6 Tell whether each number Keyis divisible 14 - All by answers 2, 3, 4, are5, 7,required and 11 for. If your the number answer isto notbe correct!divisible by these rules, enter Ø.

2, 4, 7 2, 4 2, 3, 5

2, 4, 7 3 5

7 5 3, 7

2 Ø 2, 3, 4

Ø 3 2, 3

2 2 2, 4

3, 5 5 2

Ø 3, 5 5, 7

2, 3, 4, 7 2, 4, 5 2, 3, 7

2, 4 Ø Ø

3 2, 3, 4 2, 7

2, 4, 11 2, 4 Ø

Tell whether each number isKey divisible 15- All by answers 2, 3, 4, are5, 7, required and 11 .for If yourthe number answer isto not be correct!divisible by these rules, enter Ø.

2, 3, 4 2, 3 3, 7

5 Ø 3, 11

2, 4, 5 3 2, 5, 7

2 Ø 2, 3

2 2, 3, 4 3, 5, 7

2, 3, 4 2, 4 2

Ø 2, 4 11

Ø Ø 2, 4, 5

Ø Ø 13

3 Ø 3, 5, 11

Ø 2, 3, 4, 5 2, 3, 4

Ø 3 2, 3 Tell whether each number Keyis divisible 17 - All by answers 2, 3, 4, are5, 7,required and 11 for. If your the number answer isto notbe correct!divisible by these rules, enter Ø.

3 Ø 2, 4

Ø 5, 11 2, 4, 7

2, 4 3, 7 2

2, 3, 4, 6 3 2, 4

Ø 3, 5 3,

2, 3, 4, 6 5, 7 2, 3, 6

2, 3, 4, 6 2, 3, 4, 5, 6 Ø

Ø 2, 3, 4, 6 2, 3, 4, 6, 7

3, 7 3 5

Ø 2, 4 2, 4, 7

Ø 3 2

Ø 2, 3, 5, 6 2, 4, 7

Tell whether each number isKey divisible 18 - All by answers 2, 3, 4, are5, 7, required and 11 .for If yourthe number answer is to not be divisiblecorrect! by these rules, enter Ø.

Ø 2, 3, 6 2, 3, 6, 11

2 3 3, 7

Ø 2, 4 3

2, 3, 5, 6 Ø 3, 5, 11

5 Ø 2, 11

2, 3, 6 3 5

7 3, 5 Ø

2 7 3

3 Ø 5

2, 3, 5, 6 2 5

2 3, 5 3

2, 4 2, 3, 6, 7 2 Apply the divisibility rule for 7. If the number is divisible by 7, write 7. If the number is not divisible by 7, enter Ø. Key 19

Ø Ø Ø Ø Ø

9 9 9 Ø Ø

Ø Ø Ø Ø Ø

Ø Ø Ø 9 Ø

Ø Ø 9 Ø Ø

9 9 Ø Ø 9

Ø 9 9 Ø Ø

Ø Ø 9 9 Ø

Ø 9 Ø Ø Ø

Ø Ø Ø Ø 9

Ø Ø 9 Ø Ø

Ø Ø Ø 9 Ø

Tell whether each number Keyis divisible 20 - All by answers 2, 3, 4, are5, 7,required and 11 for. If your the number answer isto notbe correct!divisible by these rules, enter Ø.

2 3 Ø

2, 7, 11 2, 4 Ø

2, 3, 4, 6, 9 7 3, 5, 7

7 3, 7, 9 2, 3, 4, 6

2 Ø 2, 3, 4, 5, 6, 10

Ø 2, 3, 5, 6, 9, 10 2, 4

3, 5, 9 2, 4 7

3, 5 2, 4, 11 Ø

2 2 Ø

Ø 2, 4 2, 4, 5, 10

2, 3, 6, 7 Ø 5

2, 3, 4, 6, 7 2, 4 2, 4

Tell whether each number isKey divisible 21 - All by answers 2, 3, 4, are5, 7, required and 11 .for If yourthe number answer is to not be divisiblecorrect! by these rules, enter Ø.

Ø 2 Ø

5 2, 4 Ø

2, 4 2, 4 Ø

2, 11 Ø Ø

2, 3, 4, 6, 11 Ø 3

2, 3, 4, 6 3 Ø

Ø 3 Ø

3, 9, 11 2, 3, 5, 6, 10 Ø

2, 3, 6, 7, 9 5 2

2, 4 2, 4 Ø

Ø Ø 11

2, 3, 4, 6, 9 2, 5, 10 2, 3, 6