The squares of prime numbers have exactly three factors.
4 has 1, 2, and 4.
9 has 1, 3, and 9.
25 has 1, 5, and 25.
49 has 1, 7, and 49.
121 has 1, 11, and 121.
169 has 1, 13, and 169.
Squares of prime numbers have exactly three factors.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
Prime squares
A number has exactly three factors if and only if it is the square of a prime number.
The squares of all prime numbers have exactly 3 factors. The numbers under fifty that are the squares of primes are 4 (1, 2, and 4), 9 (1, 3, and 9), 25 (1, 5, and 25), and 49 ( 1, 7, and 49).
All numbers that are the square of primes have exactly 3 factors.
Squares of prime numbers have exactly three factors.
Numbers with exactly three factors are squares of prime numbers.
The squares of all prime numbers above 2 have exactly 3 factors.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
Prime squares
A number has exactly three factors if and only if it is the square of a prime number.
2 and 3
3, 5 and 7
4 and 9
Prime squares have three factors. 4, 9, 25
2 4 6