62, 65, 69
60, 72, 84, 90, and 96 each have 12 factors.
The smallest number that has exactly three factors is 4.
Numbers with exactly 6 factors are perfect squares of prime numbers. The prime factorization of a number with exactly 6 factors is in the form ( p^2 ), where ( p ) is a prime number. There are 10 prime numbers less than 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. So, there are 10 numbers less than 30 that have exactly 6 factors.
24
The square of any prime number has exactly three factors: 22, 32, 52, etc.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
27
105
4, 9, 25
49 has exactly 3 factors (1, 7, and 49) and is greater than 40 and less than 60.
3*5*7*9 = 945 ...check if any number less than that has exactly four distinct factors.
It is 30.