Prime numbers have exactly two factors.
All prime numbers have only 2 factors whereas composite numbers have more than 2 factors
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That is correct -- all prime numbers have exactly two factors.
Prime numbers have only two factors.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
Prime designates numbers with exactly two factors. Composite designates numbers with more than two factors.
Squares of prime numbers have exactly three factors.