Question

relating factors and multiples i - item 23082
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 number criteria.

Step2: Analyze Jeff's statement

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

Step3: Determine correct answer

Eric's reasoning about 2 being prime (two factors: 1 and 2) is correct. Jeff's reasoning is incorrect as 2 is prime, not composite, and not all even numbers are composite.

Answer:

Eric is correct.
2 is a prime number.