QuestionConsider 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 points)
Studdy Solution
STEP 1
1. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
2. A composite number is a natural number greater than 1 that is not prime, meaning it has divisors other than 1 and itself.
3. We need to determine the primality or compositeness of the numbers 13, 16, 27, and 41.
STEP 2
1. Check if 13 is prime or composite.
2. Check if 16 is prime or composite.
3. Check if 27 is prime or composite.
4. Check if 41 is prime or composite.
STEP 3
To determine if 13 is prime, check divisibility by prime numbers less than or equal to .
- The prime numbers to check are 2 and 3.
- 13 is not divisible by 2 (since it is odd).
- 13 is not divisible by 3 (since , not an integer).
Since 13 is not divisible by any prime numbers less than or equal to , 13 is a prime number.
STEP 4
To determine if 16 is prime, check divisibility by prime numbers less than or equal to .
- The prime numbers to check are 2.
- 16 is divisible by 2 (since , an integer).
Since 16 is divisible by a prime number other than 1 and itself, 16 is a composite number.
STEP 5
To determine if 27 is prime, check divisibility by prime numbers less than or equal to .
- The prime numbers to check are 2 and 3.
- 27 is not divisible by 2 (since it is odd).
- 27 is divisible by 3 (since , an integer).
Since 27 is divisible by a prime number other than 1 and itself, 27 is a composite number.
STEP 6
To determine if 41 is prime, check divisibility by prime numbers less than or equal to .
- The prime numbers to check are 2, 3, and 5.
- 41 is not divisible by 2 (since it is odd).
- 41 is not divisible by 3 (since , not an integer).
- 41 is not divisible by 5 (since it does not end in 0 or 5).
Since 41 is not divisible by any prime numbers less than or equal to , 41 is a prime number.
The prime numbers are: 13 and 41.
The composite numbers are: 16 and 27.
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