How many positive integers less than 100 is not a factor of 2,3 and 5?
The Answer to the Question
is below this banner.
Here's the Solution to this Question
Let and denote the sets of positive integers that are divisible by 2, 3 and 5 respectively and less or equal to 100.
If and are relatively prime then a is divisible by and iff it is divisible by
It follows that and
Therefore, by Inclusion-exclusion principle, the number of positive integers that are divisible by 2 or 3 or 5 and less or equal to 100 is equal to
We conclude that the number of integers that are not divisible by 2 or 3 or 5 is equal to