Problem Description:
The task is to identify and circle all the
prime numbers and
composite numbers from the given list of numbers (1 through 50). The instructions also note that
1 is neither prime nor composite.
Solution Approach:
1.
Prime Numbers: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- Examples: 2, 3, 5, 7, etc.
- Note: 1 is
not considered a prime number.
2.
Composite Numbers: A composite number is a natural number greater than 1 that has more than two positive divisors (i.e., it can be divided evenly by numbers other than 1 and itself).
- Examples: 4, 6, 8, 9, etc.
3.
Steps to Solve:
- Identify all prime numbers between 1 and 50.
- Identify all composite numbers between 1 and 50.
- Exclude 1, as it is neither prime nor composite.
Identification of Prime Numbers:
To determine if a number is prime, check if it has any divisors other than 1 and itself. For efficiency, you only need to check divisors up to the square root of the number.
-
Prime Numbers Between 1 and 50:
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Identification of Composite Numbers:
Composite numbers are all the remaining numbers greater than 1 that are not prime.
-
Composite Numbers Between 1 and 50:
- 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50
Final Answer:
-
Prime Numbers: Circle the following numbers:
\[
\boxed{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}
\]
-
Composite Numbers: Circle the following numbers:
\[
\boxed{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50}
\]
Explanation:
-
Prime Numbers: These numbers have exactly two distinct positive divisors: 1 and the number itself.
-
Composite Numbers: These numbers have more than two distinct positive divisors.
-
Number 1: It is explicitly noted as neither prime nor composite, so it should not be circled in either section.
This completes the task. If you have any further questions, feel free to ask!
Parent Tip: Review the logic above to help your child master the concept of prime number worksheet 5th grade.
