24 and 30 - each have 8 factors.
Factors for 20 are: 1, 2, 4, 5, 10, 20
Factors for 21 are: 1, 3, 7, 21
Factors for 22 are: 1, 2, 11, 22
Factors for 23 are: 1, 23
Factors for 24 are: 1, 2, 3, 4, 6, 8, 12, 24
Factors for 25 are: 1, 5, 25
Factors for 26 are: 1, 2, 13, 26
Factors for 27 are: 1, 3, 9, 27
Factors for 28 are: 1, 2, 4, 7, 14, 28
Factors for 29 are: 1, 29
Factors for 30 are: 1, 2, 3, 5, 6, 10, 15, 30
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12, 18 and 20 each have six factors.
The factors of 16 are 1, 2, 4, 8, and 16.
16 does.
For a number to have [only] 2 factors, it must be a prime number; the prime numbers between 0 and 20 are; 2, 3, 5, 7, 11, 13, 17, 19
16