The statement is false because 2 is both an even number (divisible by 2) and a prime number (has exactly two factors: 1 and 2). It is the only even prime number, which is a well-known exception.
This statement is false because 2 itself is both even and prime, making it a counterexample to the claim. The reasoning in the statement (that divisibility by 2 rules out primality) is flawed — primality only requires no divisors other than 1 and itself, and 2 satisfies that despite being even.