Determine the number of positive integers (

Question

Determine the number of positive integers (<= 720) which are not divisible by any of 2, 3 or 5.

Accepted Answer

192 We use inclusion-exclusion to count integers up to 720 that ARE divisible by 2, 3, or 5, then subtract from 720. The key is that 720 = 2^4 * 3^2 * 5 * 1 is highly composite and divisible by 2, 3, and 5, making the multiples easy to count exactly. The complement approach: count NOT divisible by any of 2, 3, 5.