There are five whole numbers between 1 and 150 that have exactly 3 different factors. Whole numbers between 1 and 150 with exactly 3 different factors must be the square numbers whose square roots are prime.
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skip 1, not prime;
2 is prime and 2 squared is 4;
3 is prime and 3 squared is 9;
skip 4 b/c it is not prime;
5 is prime and 5 squared is 25;
6 not prime;
7 prime and 7 squared is 49;
8 not prime;
10 not prime;
11 prime and squared is 121;
12 is not prime;
13 prime, but squared it is greater than 150.
The complete list is 4, 9, 25, 49, and 121. 4 has 1, 2, 4;
9 has 1, 3, 9;
25 has 1, 5, 25 ;
49 has 1, 7, 49 ;
121 has 1, 11, 121.
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