Which of the following is the definition of a prime number?

Which of the following is the definition of a prime number?

• A. A number greater than zero that factors only into itself and 1
• B. A composite number that has multiple factors
• C. A number that is less than one
• D. A whole number that is even

Answer: (A)

The definition of a prime number is that it is a number greater than zero that can only be divided evenly by itself and the number one. This means that prime numbers have exactly two distinct positive divisors: one and the number itself. For example, 2, 3, 5, and 7 are all prime numbers because they cannot be expressed as a product of two smaller positive integers. In contrast, composite numbers (which are not primes) have more than two positive divisors, making them products of other whole numbers. Therefore, the option that states a prime number is greater than zero and factors only into itself and one accurately captures the essence of what defines prime numbers. The other options do not correctly define prime numbers. A composite number with multiple factors does not apply to the concept of prime numbers, and a number less than one cannot qualify as prime since primes must be greater than zero. Furthermore, the definition relating to whole numbers that are even does not specifically pertain to primes, as the only even prime number is 2; all other even numbers can be divided by 2, making them composite.

The definition of a prime number is that it is a number greater than zero that can only be divided evenly by itself and the number one. This means that prime numbers have exactly two distinct positive divisors: one and the number itself. For example, 2, 3, 5, and 7 are all prime numbers because they cannot be expressed as a product of two smaller positive integers.

In contrast, composite numbers (which are not primes) have more than two positive divisors, making them products of other whole numbers. Therefore, the option that states a prime number is greater than zero and factors only into itself and one accurately captures the essence of what defines prime numbers.

The other options do not correctly define prime numbers. A composite number with multiple factors does not apply to the concept of prime numbers, and a number less than one cannot qualify as prime since primes must be greater than zero. Furthermore, the definition relating to whole numbers that are even does not specifically pertain to primes, as the only even prime number is 2; all other even numbers can be divided by 2, making them composite.