2 is the only ____ number which is even.
prime
Recall the meaning of prime: A prime number has exactly two factors — \(1\) and the number itself.
Check the number 2: The factors of \(2\) are \(1\) and \(2\).
So, \(2\) has exactly two factors. Therefore, \(2\) is prime.
Also, 2 is even: An even number is any number divisible by \(2\). Clearly, \(2\div2=1\), so \(2\) is even.
Why no other even number is prime? Take any even number bigger than 2. Let it be \(n\), with \(n>2\).
Since it is even, \(n=2\times m\) for some whole number \(m\ge 2\).
That means \(2\) is a factor of \(n\) (besides \(1\) and \(n\)), so \(n\) has more than two factors.
Therefore, any even number other than \(2\) is not prime.
Conclusion: \(2\) is the only even prime number.