Understanding Prime Numbers
Exploring the concept of prime numbers and how to identify them between 1 and 100. The process involves recognizing that prime numbers have only two factors - 1 and themselves. The visual representations help in shading non-prime numbers and multiples of 2, 3, and 5. By following the rules outlined, you can easily identify and differentiate prime numbers from composite numbers within the given range.
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Presentation Transcript
A prime number has only 2 factors: 1 and itself. 1 is not a prime factor as it has only 1 factor.
Finding the prime numbers between 1 & 100.
1 2 3 4 5 6 7 8 9 10 1. Shade in 1 as it is not a prime number. 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 2. The first prime number is 2. Shade in all multiples of 2 (except 2) 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
The next prime number is 3. Colour in all multiples of 3 (not 3). Some will have already been coloured in. To check if larger numbers are factors of 3, add the digits together. If the total is a multiple of 3, then the number will be too. eg 87 8+7=15 (15 is a multiple of 3 so 87 is too)
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 91 92 93 94 95 96 97 98 99 100 Multiples of 3 Coloured in already
The next prime number is 5. Colour in all multiples of 5 (not 5). Some will have already been coloured in.
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 91 92 93 94 95 96 97 98 99 100 Multiples of 5 Coloured in already
The next prime number is 7. Colour in all multiples of 7 (not 7). Some will have already been coloured in.
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 91 92 93 94 95 96 97 98 99 100 Multiples of 7 Coloured in already
The next prime number is 11. However 11 x 11=121 121>100 There is no need to check for multiples of 11 if all the multiples of 2,3,5 & 7 have been coloured in. The remaining numbers are all prime numbers. There should be 25 of them.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Prime numbers between 1 - 100
Extension: finding the prime numbers 101-200.
Besides finding multiples of 2,3,5 & 7, what other prime numbers will you need to find multiples of? Check the squares of the next few prime numbers:11, 13 & 17
11 x 11= 13 x 13= 17 x 17= 121 <200 169 <200 289 >200 Yes Yes No
Finding prime numbers between 101-200 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Prime numbers 101-200 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 Multiples of 2
Prime numbers 101-200 101 102 103 104 105 106 107 108 109 110 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 151 152 153 154 155 156 157 158 159 60 161 162 163 164 165 166 167 168 169 170 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 191 192 193 194 195 196 197 198 199 200 Multiples of 3 Coloured in already
Prime numbers 101-200 101 102 103 104 105 106 107 108 109 110 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 151 152 153 154 155 156 157 158 159 60 161 162 163 164 165 166 167 168 169 170 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 191 192 193 194 195 196 197 198 199 200 Multiples of 5 Coloured in already
Prime numbers 101-200 101 102 103 104 105 106 107 108 109 110 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 151 152 153 154 155 156 157 158 159 60 161 162 163 164 165 166 167 168 169 170 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 191 192 193 194 195 196 197 198 199 200 Multiples of 7 Coloured in already
Prime numbers 101-200 101 102 103 104 105 106 107 108 109 110 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 151 152 153 154 155 156 157 158 159 60 161 162 163 164 165 166 167 168 169 170 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 191 192 193 194 195 196 197 198 199 200 Multiples of 11 Coloured in already
Prime numbers 101-200 101 102 103 104 105 106 107 108 109 110 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 151 152 153 154 155 156 157 158 159 60 161 162 163 164 165 166 167 168 169 170 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 191 192 193 194 195 196 197 198 199 200 Multiples of 13 Coloured in already
Prime numbers 101-200 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 60 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Make a tally chart of the number of prime numbers in each 25 block: Tally Frequency 1-25 26-50 51-75 76-100 101-125 126-150 151-175 176-200 Draw a bar chart of your results.
Make an intelligent estimate of how many prime numbers there will be in the next four 25 blocks: 201-225 226-250 251-275 276-300 (answers on next slide)
Range 201-225 226-250 251-275 276-300 Prime numbers 211,223 227,229,233,239,241 251,257,263,269,271 277,281,283,293 Frequency 2 5 5 4
Make a tally chart of the last digit (units) of each prime number between 1-200 Last digit 0 1 2 3 4 5 6 7 8 9 Tally Frequency Draw a graph of your results.
a) Which 4 digits are never at the end of a prime number? b) Which 2 digits are only each found at the end of one prime number? c) Which four digits do most prime numbers end with? d) Which is the most common digit in the units column of prime numbers?
Finally: choose a prime number (not 2) Square it. + 5 8 What is the remainder?
