Numbers not divisible by 2,3,5,7,9 below 100

Since any number divisible by 9 is already divisible by 3, we only need to find numbers \le 100 that are not divisible by 2, 3, 5, or 7. Numbers coprime to all prime numbers up to ⟨MATH⟩√(100)⟨/MATH⟩ (which is 10) are either the number 1 or prime numbers themselves. The prime numbers greater than 7 and less than 100 are: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. This gives us exactly 21 prime numbers. Adding the number 1 gives a total count of 21 + 1 = 22.

Answer: (c).