Advanced Placement (AP) Computer Science

Which of the following describes a prime number?

1. A number that can be divided by two

2. A number that has more than two distinct positive divisors

3. A number divisible only by itself and one

4. A number that is a perfect square

The correct answer is: A number divisible only by itself and one

A prime number is specifically defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. This means that a prime number can only be divided evenly by 1 and the number itself, resulting in exactly two distinct positive divisors. Option C captures this definition perfectly by stating that a prime number is divisible only by itself and one. For instance, the number 5 is prime because it can only be evenly divided by 1 and 5. The other options do not align with the characteristics of prime numbers. For example, numbers that can be divided by two, such as even numbers like 4, are not necessarily prime since they can have additional divisors. Similarly, a number with more than two distinct positive divisors, like 6 (which is divisible by 1, 2, 3, and 6), is not prime. Lastly, a perfect square, such as 9 or 16, has an odd number of divisors due to the square root being repeated (for example, 9 is divisible by 1, 3, and 9), which again does not conform to the definition of prime numbers. Hence, option C accurately identifies what constitutes a prime number