Final answer:
The numbers 13 and 41 are prime because they have no divisors other than 1 and themselves. The numbers 16 and 27 are composite because they can be divided by numbers other than 1 and themselves.
Step-by-step explanation:
To determine which of the numbers are prime and which are composite, we look at whether they have more divisors other than 1 and themselves.
A prime number has exactly two distinct natural number divisors: 1 and itself. A composite number has more than two divisors.
- 13 is a prime number because its only divisors are 1 and 13.
- 16 is a composite number because it can be divided by 1, 2, 4, 8, and 16.
- 27 is a composite number as it has divisors of 1, 3, 9, and 27.
- 41 is a prime number with divisors only being 1 and 41.
Therefore, 13 and 41 are prime, while 16 and 27 are composite numbers.