There are an infinite number of them. 8 has three prime factors, 30 is the first with three distinct prime factors.
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A number has exactly three factors if and only if it is the square of a prime number.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
3 is a prime number because it has exactly two factors which are whole numbers: itself and one. This is the definition of a prime.
A prime number, like 2, 3 or 5.
There are an infinite number of prime factorizations with exactly three factors. Without something more specific, we won't be able to narrow it down.