How many integers between 1 and 280, inclusive, are not divisible by 2, 3, or 5?
+128474 Number divisible by 2 = floor [ 280 /2] = 140
Number divisible by 3 = floor [ 280/3 ] = 93
Number divisible by 5 = floor [ 280 / 5] = 56
Number divisible by 2* 3 = floor [ 280 / 6 ] = 46
Number divisible by 2*5 = floor [ 280 / 10 ] = 28
Number divisible by 3*5 = floor [ 280 / 15] = 18
Number divisible by 2 * 3 * 5 = floor [ 280 / 30 ] = 9
N ( divisible by 2 or 3 or 5) =
140 + 93 + 56 - 46 - 28 - 18 - 9 = 188
Number NOT divisible by 2, 3 or 5 = 280 - 188 = 92
1 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 49 , 53 , 59 , 61 , 67 , 71 , 73 , 77 , 79 , 83 , 89 , 91 , 97 , 101 , 103 , 107 , 109 , 113 , 119 , 121 , 127 , 131 , 133 , 137 , 139 , 143 , 149 , 151 , 157 , 161 , 163 , 167 , 169 , 173 , 179 , 181 , 187 , 191 , 193 , 197 , 199 , 203 , 209 , 211 , 217 , 221 , 223 , 227 , 229 , 233 , 239 , 241 , 247 , 251 , 253 , 257 , 259 , 263 , 269 , 271 , 277 , Total = 74 such numbers
