Question

eric said that the number 2 is prime because it has only two factors.
jeff said that the number 2 is composite because it is even, and all even
numbers are composite.

who is correct?

eric is correct.
2 is a prime number.

jeff is correct.
2 is a composite number.

both of them are correct.
2 is both a prime and a composite number.

neither of them is correct.
2 is neither a prime nor a composite number.

Explanation:

Step1: Recall prime number definition

A prime number is a number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For 2, the factors are 1 and 2, so it meets the prime definition.

Step2: Analyze Jeff's claim

A composite number is a positive integer that has at least one positive divisor other than 1 and itself. 2 only has 1 and 2 as divisors, so it's not composite. Also, not all even numbers are composite (e.g., 2 is even and prime). So Jeff is wrong.

Step3: Evaluate options

Eric's statement aligns with the prime definition of 2. Other options (Jeff correct, both correct, neither correct) are inconsistent with number theory definitions.

Answer:

A. Eric is correct. 2 is a prime number.