Kaplan Nursing Entrance Practice Exam

Which of the following statements about prime numbers is true?

1. A prime number can only be formed by two factors.

2. All prime numbers are even.

3. A prime number can be negative.

4. 1 is the smallest prime number.

The correct answer is: A prime number can only be formed by two factors.

A prime number is defined as a natural number greater than one that cannot be formed by multiplying two smaller natural numbers. This means that a prime number has exactly two distinct positive factors: 1 and itself. For instance, the number 5 is prime because its only divisors are 1 and 5. Therefore, the assertion that a prime number can only be formed by two factors is indeed true. The other statements do not hold true in the context of prime numbers. Not all prime numbers are even; in fact, the only even prime number is 2, as any other even number can be divided by 2 and thus has at least three factors (1, 2, and itself). The idea that a prime number can be negative is also incorrect because the definition of prime numbers restricts them to positive integers greater than one. Lastly, 1 is not considered a prime number; the smallest prime number is 2. Thus, the correct understanding is that a prime number has precisely two factors, reinforcing the correctness of the first statement.