This question has two parts, Part A and Part B.

To answer your question about the numbers 13, 16, 27, and 41, let's look at each part separately.

Part A: Which of these numbers are prime? How do you know? A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself.

• 13: The only divisors are 1 and 13. Therefore, 13 is prime.
• 16: The divisors are 1, 2, 4, 8, and 16. Since it has divisors other than 1 and itself, 16 is not prime.
• 27: The divisors are 1, 3, 9, and 27. Since it has divisors other than 1 and itself, 27 is not prime.
• 41: The only divisors are 1 and 41. Therefore, 41 is prime.

Conclusion for Part A: The prime numbers among 13, 16, 27, and 41 are 13 and 41.

Part B: Which of these numbers are composite? How do you know? A composite number is defined as a number greater than 1 that has more than two positive divisors.

• 13: As established, it has only two divisors (1 and 13), so it is not composite.
• 16: The divisors are 1, 2, 4, 8, and 16. Since it has more than two divisors, 16 is composite.
• 27: The divisors are 1, 3, 9, and 27. Since it has more than two divisors, 27 is composite.
• 41: As established, it has only two divisors (1 and 41), so it is not composite.

Conclusion for Part B: The composite numbers among 13, 16, 27, and 41 are 16 and 27.