What numbers have only four factors?

Answer 1

A number with two prime factors that are not the same will have only four factors. It will have 1, itself, and those two prime factors as its factors.

Examples:

6 = 2 x 3. Its factors are 1, 2, 3, and 6.

15 = 3 x 5. Its factors are 1, 3, 5, and 15.

77 = 7 x 11. Its factors are 1, 7, 11, and 77.

Counter-examples:

4 = 2 x 2. Its factors are 1, 2, and 4.

12 = 2 x 2 x 3. Its factors are 1, 2, 3, 4, 6, and 12.

30 = 2 x 3 x 5. Its factors are 1, 2, 3, 5, 6, 10, 15, and 30.

45 = 3 x 3 x 5. Its factors are 1, 3, 5, 9, 15, and 45.

Answer 2

Prime numbers to the third power, like 8 and 27.

Answer 3

There are an infinite number of numbers with only four factors, started by 6, 8 and 10.

Answer 4

There are quite a few. 6 does. 8 does.