Prime and Composite Numbers Chart 1-100

Problem Description:

The image provided is a worksheet titled "Prime and Composite Numbers." It contains a grid of numbers from 1 to 100, with three columns labeled:
- Prime: Numbers that are prime.
- Composite: Numbers that are composite.
- Neither Prime nor Composite: Numbers that do not fit into either category.

The task is to classify each number in the grid into one of these three categories.

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Solution Approach:

1. 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.
- Neither Prime nor Composite: The number 1, as it does not meet the criteria for being prime or composite.

2. Steps to Solve:
- Identify all prime numbers between 1 and 100.
- Identify all composite numbers between 1 and 100.
- Classify the number 1 as "Neither Prime nor Composite."

3. Prime Number Identification:
- Use the Sieve of Eratosthenes or manually check divisibility by numbers less than the square root of each number.
- Prime numbers between 1 and 100 are:
\( 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 \).

4. Composite Number Identification:
- Any number greater than 1 that is not prime is composite.
- Examples include: \( 4, 6, 8, 9, 10, 12, \ldots, 100 \).

5. Classification:
- Place each number in the appropriate column:
- Prime: All prime numbers.
- Composite: All composite numbers.
- Neither Prime nor Composite: The number 1.

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Classification of Numbers:

#### Prime Numbers:
- \( 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 \)

#### Composite Numbers:
- All other numbers greater than 1 that are not prime. For example:
- \( 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, \ldots, 100 \)

#### Neither Prime nor Composite:
- \( 1 \)

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Final Answer:

The completed worksheet would have:
- Prime Column: Contains all prime numbers listed above.
- Composite Column: Contains all composite numbers.
- Neither Prime nor Composite Column: Contains the number 1.

\[
\boxed{\text{See classification above.}}
\]