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# help counting

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220
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How many integers between 1 and 280, inclusive, are not divisible by 2, 3, or 5?

Jul 12, 2022

#1
+126978
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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

Jul 12, 2022
#2
0

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

Jul 12, 2022