Prime numbers have exactly 2 factors, themselves and 1.
If you square a prime number, it will have those 2 factors, plus one additional
factor, which is that prime number itself. That makes 3 factors.

So we only list the squares of prime up through the biggest square of a prime
that does not exceed 567. So we find the square root of 567, which is about
23.8. So the biggest prime we will need to square is 23.

 1. 2² = 4, which has three factors, 1,2, and 4.
 2. 3² = 9, which has three factors, 1,3, and 9.
 3. 5² = 25, which has three factors, 1,5, and 25.
 4. 7² = 49, which has three factors, 1,7, and 49.
 5. 11² = 121, which has three factors, 1,11, and 121.
 6. 13² = 169, which has three factors, 1,13, and 169.
 7. 17² = 289, which has three factors, 1,17, and 289.
 8. 19² = 361, which has three factors, 1,19, and 361.
 9. 23² = 529, which has three factors, 1,23, and 529.

So the answer is 9 of them.

Edwin