25
No numbers between 1 and 100 have exactly eleven factors. 60, 72, 84, 90 and 96 each have twelve factors.
Three numbers.
There are three of them with exactly five factors.
Squares of prime numbers have only three factors.
Composite numbers
There are three numbers that fit those requirements.
The numbers with only three factors are squares of prime numbers.
Numbers with exactly three factors are squares of prime numbers.
Factors don't have numbers. Numbers have factors. Numbers that have the factors 2, 4 and 8 are 8 and all of its multiples.
A prime number has no other factors except itself and 1. There are three numbers between 80 and 100 that are prime: 83, 89 and 97.
Squares of prime numbers have exactly three factors.
There are no prime numbers with three factors. By definition, a prime number has exactly two factors - 1 and itself.