Problem
COM-B2-M02-P006 Not Divisible by \(2,3,5\)
#6
★★★☆☆ Level 3 of 5
How many integers from \(1\) to \(1000\) are divisible by none of \(2,3,5\)?
First count numbers divisible by at least one of \(2,3,5\).
The number divisible by at least one of \(2,3,5\) is \(500+333+200-166-100-66+33=734\). Therefore the number divisible by none of them is \(1000-734=266\).
Two steps: inclusion-exclusion and complement.