document.write( "Question 1025865: How many numbers from 1-1000 are there that are not divisible by any of the digits 2,3,5. \n" ); document.write( "

Algebra.Com's Answer #641200 by KMST(5328) $\"\"$ $\"About$

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Among the numbers 1 - 1000 ,
\n" ); document.write( " $\"1000%2F2=500\"$ are divisible by $\"2\"$ ;
\n" ); document.write( " $\"1000%2F5=200\"$ are divisible by $\"5\"$ ,
\n" ); document.write( "and since $\"1000%2F3=333%261%2F3\"$ ,
\n" ); document.write( " $\"333\"$ are divisible by $\"3\"$ .
\n" ); document.write( " $\"1000%2F%282%2A5%29=1000%2F10=100\"$ are divisible by $\"2\"$ and $\"5\"$ ;
\n" ); document.write( " $\"166\"$ are divisible by $\"2\"$ and $\"3\"$
\n" ); document.write( "(because $\"1000%2F%282%2A3%29=1000%2F6=166%262%2F3\"$ ),
\n" ); document.write( "and since $\"1000%2F%283%2A5%29=1000%2F15=66%262%2F3\"$ ,
\n" ); document.write( " $\"66\"$ are divisible by $\"3\"$ and $\"5\"$ .
\n" ); document.write( "Also, since $\"1000%2F%282%2A3%2A5%29=1000%2F30=33%261%2F3\"$ ,
\n" ); document.write( " $\"33\"$ of the numbers 1 - 1000 are divisible by $\"2\"$ , $\"3\"$ and $\"5\"$ .
\n" ); document.write( "So the numbers from 1 through 100 that are not divisible by any of the digits 2, 3, and 5 are
\n" ); document.write( " $\"1000-500-200-333%2B100%2B166%2B66-33=highlight%28266%29\"$ \n" ); document.write( "

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