Which of the following defines a prime number?

Which of the following defines a prime number?

• A. A number that can be divided evenly by 1 or itself and other numbers
• B. A number that can only be divided evenly by 1 or itself
• C. A number that is greater than 1 and has a negative divisor
• D. A number that is less than 1 and has no positive divisors

Answer: (B)

A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. This means that a prime number has exactly two distinct positive divisors: 1 and itself. The definition encapsulates the fundamental trait of prime numbers, which is that they are only divisible by these two numbers without leaving a remainder. In contrast, the first choice describes a number that can be divided by more than just 1 and itself, which would include composite numbers—numbers that have additional divisors. The third choice refers to a number with a negative divisor, which is outside the standard definition of prime numbers and is irrelevant since prime classification applies only to positive integers greater than 1. The fourth option talks about a number less than 1, which does not fit the criteria for prime numbers, as prime numbers must be greater than 1. Thus, identifying a prime number correctly hinges on recognizing that it is exclusively divisible by 1 and itself, making the definition provided in the selected answer accurate.

A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. This means that a prime number has exactly two distinct positive divisors: 1 and itself. The definition encapsulates the fundamental trait of prime numbers, which is that they are only divisible by these two numbers without leaving a remainder.

In contrast, the first choice describes a number that can be divided by more than just 1 and itself, which would include composite numbers—numbers that have additional divisors. The third choice refers to a number with a negative divisor, which is outside the standard definition of prime numbers and is irrelevant since prime classification applies only to positive integers greater than 1. The fourth option talks about a number less than 1, which does not fit the criteria for prime numbers, as prime numbers must be greater than 1.

Thus, identifying a prime number correctly hinges on recognizing that it is exclusively divisible by 1 and itself, making the definition provided in the selected answer accurate.