What is a characteristic of a prime number?

What is a characteristic of a prime number?

• A. It has more than two factors
• B. It can be divided by any number
• C. It is greater than one and has exactly two factors
• D. It is always an even number

Answer: (C)

A prime number is defined as a natural number greater than one that has exactly two distinct positive factors: one and itself. This characteristic is crucial in number theory, as it makes prime numbers the building blocks of the integers. Every prime number can only be divided evenly by 1 and the number itself, which means that no other numbers can divide a prime number without leaving a remainder. For instance, consider the prime number 5; it can only be divided evenly by 1 and 5. This definition is fundamental for various mathematical concepts, including factorization and the development of more advanced topics in mathematics. The statement correctly conveys this essential property of prime numbers, distinguishing them from composite numbers, which have more than two factors.

A prime number is defined as a natural number greater than one that has exactly two distinct positive factors: one and itself. This characteristic is crucial in number theory, as it makes prime numbers the building blocks of the integers. Every prime number can only be divided evenly by 1 and the number itself, which means that no other numbers can divide a prime number without leaving a remainder.

For instance, consider the prime number 5; it can only be divided evenly by 1 and 5. This definition is fundamental for various mathematical concepts, including factorization and the development of more advanced topics in mathematics. The statement correctly conveys this essential property of prime numbers, distinguishing them from composite numbers, which have more than two factors.