The number of positive integers not greater than 100, having exactly four distinct factors other than 1 and the number itself, is:Enter your response (as an integer) using the virtual keyboard in the box provided below.

The question is asking for the number of positive integers less than or equal to 100 that have exactly four distinct factors other than 1 and the number itself.

A number has exactly four distinct factors other than 1 and itself if and only if it is a product of two distinct prime numbers. This is because a prime number has exactly two distinct factors, 1 and itself. So, the product of two distinct prime numbers will have exactly four distinct factors: 1, the two prime numbers, and the product itself.

The prime numbers less than or equal to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

We need to find pairs of these prime numbers whose product is less than or equal to 100. The pairs are: (2, 3), (2, 5), (2, 7), (2, 11), (2, 13), (2, 17), (2, 19), (2, 23), (2, 29), (2, 31), (2, 37), (2, 41), (2, 43), (2, 47), (3, 5), (3, 7), (3, 11), (3, 13), (3, 17), (3, 19), (3, 23), (3, 29), (3, 31), (5, 7), (5, 11), (5, 13), (5, 17), (5, 19), (7, 11), (7, 13), (11, 7).

So, there are 30 positive integers not greater than 100 that have exactly four distinct factors other than 1 and the number itself.