8 of them.
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2 is the only member of both the set of all prime numbers and the set of all even numbers.
Many infinite sets appear in mathematics: the set of counting numbers; the set of integers; the set of rational numbers; the set of irrational numbers; the set of real numbers; the set of complex numbers. Also, certain subsets of these, such as the set of square numbers, the set of prime numbers, and others.
The set of even numbers contains the prime number, 2. The set of composite numbers contains infinitely many odd numbers.
Finite, no.
Any set of prime numbers has a GCF of 1, which is the technical definition of being relatively prime but it's a bit redundant. The members of that set are already prime.