When is a number neither prime nor composite?

When is a number neither prime nor composite?

• A. When it is 0
• B. When it is 1
• C. When it is a negative number
• D. When it is greater than 1

Answer: (B)

A number is considered neither prime nor composite when it is 1. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself, while a composite number is a natural number greater than 1 that has additional divisors. Since 1 only has one positive divisor, which is itself, it does not fit the definitions of prime or composite. This unique status sets 1 apart from all other natural numbers. Other choices do not meet the criteria for being neither prime nor composite: 0 is not classified in either category within the context of the natural number system; negative numbers do not fall under the definitions of prime or composite either, as these concepts apply solely to positive integers greater than 1; and numbers greater than 1 are either prime or composite by definition. Thus, 1 is the only number that is explicitly categorized as neither prime nor composite.

A number is considered neither prime nor composite when it is 1. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself, while a composite number is a natural number greater than 1 that has additional divisors.

Since 1 only has one positive divisor, which is itself, it does not fit the definitions of prime or composite. This unique status sets 1 apart from all other natural numbers.

Other choices do not meet the criteria for being neither prime nor composite: 0 is not classified in either category within the context of the natural number system; negative numbers do not fall under the definitions of prime or composite either, as these concepts apply solely to positive integers greater than 1; and numbers greater than 1 are either prime or composite by definition. Thus, 1 is the only number that is explicitly categorized as neither prime nor composite.