How many integers x, with 0 < x ≤ 100, are divisible by 2, 3 and 4?
To count the number of integers x that are divisible by 2, 3, and 4, we need to find the least common multiple (LCM) of 2, 3, and 4.
The prime factorization of 2 is 2.
The prime factorization of 3 is 3.
The prime factorization of 4 is 2 * 2.
To find the LCM, we take the highest power of each prime that appears in the factorizations. In this case, it is 2 * 2 * 3 = 12.
Therefore, there are 100/12 = <<100/12=8>>8 integers x, with 0 < x ≤ 100, that are divisible by 2, 3, and 4. Answer: \boxed{8}.