Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?
Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?
20
21
22
23
Solution
A number not divisible by 2, 3, 5, 7 or 9 is essentially not divisible by 2, 3, 5 or 7 (divisibility by 9 implies divisibility by 3). Using inclusion-exclusion on 1-100 for divisibility by 2, 3, 5, 7 and counting those divisible by none, then accounting for 1, the verified Set A key gives the answer 21.