Consider the numbers 13, 16, 27, and 41. %0D%0Aa. Which of these numbers are prime? How do you know?%0D%0Ab. Which of these numbers are composite? How do you know
a. To determine if a number is prime or not, we need to check if it is divisible by any number other than 1 and itself.
Out of the given numbers:
- 13: It is only divisible by 1 and 13, so it is a prime number.
- 16: It is divisible by 1, 2, 4, 8, and 16, so it is not a prime number.
- 27: It is divisible by 1, 3, 9, and 27, so it is not a prime number.
- 41: It is only divisible by 1 and 41, so it is a prime number.
Therefore, the prime numbers in the given set are 13 and 41.
b. A composite number is a positive integer that has divisors other than 1 and itself.
Out of the given numbers:
- 13: It is a prime number and does not have any divisors other than 1 and 13, so it is not composite.
- 16: It is divisible by 1, 2, 4, 8, and 16, so it is a composite number.
- 27: It is divisible by 1, 3, 9, and 27, so it is a composite number.
- 41: It is a prime number and does not have any divisors other than 1 and 41, so it is not composite.
Therefore, the composite numbers in the given set are 16 and 27.