A Prime number, like 2, 3 or 5.
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A prime number has exactly two factors.
That's a prime number.
A prime number has exactly two factors, 1 and itself. A composite number has more than two factors.
1 is the only number that has exactly one factor. A prime number has exactly two factors, 1 and the number itself. A composite number has more than two factors.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.