How many numbers less than 100 have exactly four factors?

Numbers having 4 factors are either of the form $$a^3\ or\ ab$$ where a and b are prime factors.
Numbers of the form $$a^3$$ which are less than 100 are: 8 and 27 = 2 numbers.
To find the numbers of the form ab, we will assume values for "a".
Case 1: a = 2. For ab to be lower than 100, "b" can take values 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47 = 14 numbers.
Case 2: a = 3. For ab to be lower than 100, "b" can take values 5, 7, 11, 13, 17, 19, 23, 29 and 31 = 9 numbers.
Case 3: a = 5. For ab to be lower than 100, "b" can take values 7, 11, 13, 17 and 19 = 5 numbers.
Case 4: a = 7. For ab to be lower than 100, "b" can take values 11 and 13 = 2 numbers.
No other cases are possible.
So total cases possible for numbers lower than 100 having 4 factors are 2 + 14 + 9 + 5 + 2 = 32.