31, 37, 41, 43, 47
Pick three.
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31 37 47
Each of the 25 prime numbers from 1 to 100 has exactly two factors, 1 and the number itself. The other 75 numbers from 1 to 100 are not prime numbers because none of them have exactly two factors.
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.
4 and 9
The list of prime numbers is infinite. There are two factors for each.