How many numbers less than 240 are not divisible by 2, 3, or 5?

Question

Mathematics

How to solve this problem on paper?

Answer 1

Count those that are divisible by at least one. It should be borne in mind that some numbers will be counted several times. You need to use the inclusion-exclusion formula .
Total divisible by at least one of these numbers:
240/2 + 240/3 + 240/5 - 240/(2*3) - 240/(2*5) - 240/(3*5) + 240/(2 *3*5) = 176
So, non-fissile 240 - 176 = 64
Check:

ghci> length $ filter (\x -> 0 `notElem` [x `mod` 2, x `mod` 3, x `mod` 5]) [1..240]
64

Answer 2

python

In [4]: 240 - len([x for x in range(1, 241) if x % 2 == 0 and x % 3 and x % 5])
Out[4]: 176