Question 1025865
Among the numbers 1 - 1000 ,
{{{1000/2=500}}} are divisible by {{{2}}} ;
{{{1000/5=200}}} are divisible by {{{5}}} ,
and since {{{1000/3=333&1/3}}} ,
{{{333}}} are divisible by {{{3}}} .
{{{1000/(2*5)=1000/10=100}}} are divisible by {{{2}}} and {{{5}}} ;
{{{166}}} are divisible by {{{2}}} and {{{3}}}
(because {{{1000/(2*3)=1000/6=166&2/3}}} ),
and since {{{1000/(3*5)=1000/15=66&2/3}}} ,
{{{66}}} are divisible by {{{3}}} and {{{5}}} .
Also, since {{{1000/(2*3*5)=1000/30=33&1/3}}} ,
{{{33}}} of the numbers 1 - 1000 are divisible by {{{2}}} , {{{3}}} and {{{5}}} .
So the numbers from 1 through 100 that are not divisible by any of the digits 2, 3, and 5 are
{{{1000-500-200-333+100+166+66-33=highlight(266)}}}