What is a primary characteristic of a prime number?

What is a primary characteristic of a prime number?

• A. It can be divided evenly by multiple numbers
• B. It has exactly two distinct positive divisors: 1 and itself
• C. It is an even number
• D. It is greater than 10

Answer: (B)

A primary characteristic of a prime number is that it has exactly two distinct positive divisors: 1 and itself. This definition establishes prime numbers as the building blocks of the natural numbers since they cannot be formed by multiplying two smaller natural numbers other than 1 and the prime number itself. For instance, the number 7 is prime because the only divisors are 1 and 7. In contrast, composite numbers are defined as having more than two positive divisors, demonstrating the uniqueness of prime numbers in the set of natural numbers. The first option suggests that a prime number can be divided evenly by multiple numbers, which contradicts the definition of primacy. The third option incorrectly states that a prime number is an even number, although the only even prime number is 2; all other even numbers are composite. The last option erroneously claims that prime numbers must be greater than 10, as there are numerous primes less than 10, such as 2, 3, 5, and 7. Thus, the correct answer highlights the fundamental definition of a prime number.

A primary characteristic of a prime number is that it has exactly two distinct positive divisors: 1 and itself. This definition establishes prime numbers as the building blocks of the natural numbers since they cannot be formed by multiplying two smaller natural numbers other than 1 and the prime number itself.

For instance, the number 7 is prime because the only divisors are 1 and 7. In contrast, composite numbers are defined as having more than two positive divisors, demonstrating the uniqueness of prime numbers in the set of natural numbers.

The first option suggests that a prime number can be divided evenly by multiple numbers, which contradicts the definition of primacy. The third option incorrectly states that a prime number is an even number, although the only even prime number is 2; all other even numbers are composite. The last option erroneously claims that prime numbers must be greater than 10, as there are numerous primes less than 10, such as 2, 3, 5, and 7. Thus, the correct answer highlights the fundamental definition of a prime number.