Prime and Composite Numbers Worksheets - 15 Worksheets Library - Free Printable

Problem Description:

The task is to sort the given numbers into two categories: Prime Numbers and Composite Numbers. The numbers provided are from 1 to 50.

Definitions:

- Prime Number: A number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
- Composite Number: A number greater than 1 that has more than two distinct positive divisors.
- Note: The number 1 is neither prime nor composite.

Solution Approach:

1. Identify Prime Numbers:
- Check each number from 2 to 50 to see if it has exactly two divisors (1 and itself).
- Use divisibility rules or trial division to determine primality.

2. Identify Composite Numbers:
- Any number greater than 1 that is not a prime number is a composite number.

3. Exclude the Number 1:
- Since 1 is neither prime nor composite, it should be excluded from both columns.

Step-by-Step Solution:

#### Prime Numbers:
- Start with 2 (the smallest prime number) and check each subsequent number up to 50.
- Use trial division by checking divisibility by all integers 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

#### Composite Numbers:
- Any number greater than 1 that is not a prime number is composite.
- Exclude the number 1.

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:
$$
\boxed{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}
$$

#### Composite 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 no divisors other than 1 and themselves. For example, 7 is only divisible by 1 and 7.
- Composite Numbers: These numbers have additional divisors besides 1 and themselves. For example, 6 is divisible by 1, 2, 3, and 6.
- Number 1: It is neither prime nor composite, so it is not included in either category.

This分类确保了所有数字都被正确地归类。