Prime versus composite: Which statement correctly distinguishes composite and prime numbers?

Prime versus composite: Which statement correctly distinguishes composite and prime numbers?

• A. A prime number has exactly two factors; a composite has more than two.
• B. A composite number has exactly two factors; a prime has more than two.
• C. A prime number has more than two factors; a composite has exactly two.
• D. A composite number has no factors other than 1 and itself.

Answer: (A)

Whether a number is prime or composite hinges on how many positive divisors it has. A prime number is only divisible by 1 and itself, so it has exactly two factors. A composite number can be divided by more than just 1 and itself, so it has more than two factors. This makes the statement that primes have exactly two factors and composites have more than two the correct description. For the other possibilities: saying a composite has exactly two factors would make it prime, not composite. Saying a prime has more than two factors contradicts the definition of a prime. And saying a composite has no factors other than 1 and itself describes primes, not composites. For example, 7 is prime (factors 1 and 7), while 12 is composite (factors 1, 2, 3, 4, 6, 12).

Whether a number is prime or composite hinges on how many positive divisors it has. A prime number is only divisible by 1 and itself, so it has exactly two factors. A composite number can be divided by more than just 1 and itself, so it has more than two factors. This makes the statement that primes have exactly two factors and composites have more than two the correct description.

For the other possibilities: saying a composite has exactly two factors would make it prime, not composite. Saying a prime has more than two factors contradicts the definition of a prime. And saying a composite has no factors other than 1 and itself describes primes, not composites. For example, 7 is prime (factors 1 and 7), while 12 is composite (factors 1, 2, 3, 4, 6, 12).