Consider the numbers 13, 16, 27, and 41.
a. Which of these numbers are prime? How do you know?
b. Which of these numbers are composite? How do you know?(2 point)
a. Prime numbers are numbers that have only two distinct positive divisors: 1 and the number itself. We can determine whether each of these numbers is prime through a process of elimination by checking for divisors.
- 13 is a prime number. It has no divisors other than 1 and 13 itself. If it were divisible by any other number (2-12), we would have found a factor by now, but there are none.
- 16 is not a prime number. It is a composite number because it has divisors other than 1 and itself. In particular, it is divisible by 2 (2 x 8 = 16), 4 (4 x 4 = 16), and 8 (8 x 2 = 16).
- 27 is not a prime number. It is a composite number because it has divisors other than 1 and itself. Specifically, it is divisible by 3 (3 x 9 = 27).
- 41 is a prime number. Like with 13, there are no divisors other than 1 and 41, and it isn't divisible by any numbers between 2 and 40.
b. Composite numbers are numbers that have more divisors than just 1 and the number itself.
- As mentioned above, 16 and 27 are composite numbers because they have several divisors aside from just 1 and themselves:
- 16 has divisors of 2, 4, and 8.
- 27 has a divisor of 3 (and 9).
So, to summarize:
- The prime numbers from the list are: 13 and 41
- The composite numbers from the list are: 16 and 27