Factors worksheet for students to practice identifying factors and prime numbers up to 24.

Problem Overview:

The task is to complete a table listing the factors of all numbers from 1 to 24. Additionally, we need to identify and highlight the prime numbers (numbers with exactly two factors: 1 and themselves) in the range from 1 to 24.

Solution Approach:

1. Understand Factors: A factor of a number is any integer that divides the number exactly without leaving a remainder.
2. List Factors for Each Number: For each number from 1 to 24, determine all its factors.
3. Identify Prime Numbers: After listing the factors, identify which numbers have exactly two factors (1 and the number itself).

Step-by-Step Solution:

#### Listing Factors for Each Number:
We will list the factors for each number from 1 to 24.

- Number 1: Factors = \(1\)
- Number 2: Factors = \(1, 2\) (Prime)
- Number 3: Factors = \(1, 3\) (Prime)
- Number 4: Factors = \(1, 2, 4\)
- Number 5: Factors = \(1, 5\) (Prime)
- Number 6: Factors = \(1, 2, 3, 6\)
- Number 7: Factors = \(1, 7\) (Prime)
- Number 8: Factors = \(1, 2, 4, 8\)
- Number 9: Factors = \(1, 3, 9\)
- Number 10: Factors = \(1, 2, 5, 10\)
- Number 11: Factors = \(1, 11\) (Prime)
- Number 12: Factors = \(1, 2, 3, 4, 6, 12\)
- Number 13: Factors = \(1, 13\) (Prime)
- Number 14: Factors = \(1, 2, 7, 14\)
- Number 15: Factors = \(1, 3, 5, 15\)
- Number 16: Factors = \(1, 2, 4, 8, 16\)
- Number 17: Factors = \(1, 17\) (Prime)
- Number 18: Factors = \(1, 2, 3, 6, 9, 18\)
- Number 19: Factors = \(1, 19\) (Prime)
- Number 20: Factors = \(1, 2, 4, 5, 10, 20\)
- Number 21: Factors = \(1, 3, 7, 21\)
- Number 22: Factors = \(1, 2, 11, 22\)
- Number 23: Factors = \(1, 23\) (Prime)
- Number 24: Factors = \(1, 2, 3, 4, 6, 8, 12, 24\)

#### Identifying Prime Numbers:
Prime numbers are those with exactly two factors: 1 and the number itself. From the list above, the prime numbers between 1 and 24 are:
- 2, 3, 5, 7, 11, 13, 17, 19, 23

Completed Table:

Here is the completed table:

| NUMBER | FACTORS |
|--------|------------------|
| 1 | 1 |
| 2 | 1, 2 |
| 3 | 1, 3 |
| 4 | 1, 2, 4 |
| 5 | 1, 5 |
| 6 | 1, 2, 3, 6 |
| 7 | 1, 7 |
| 8 | 1, 2, 4, 8 |
| 9 | 1, 3, 9 |
| 10 | 1, 2, 5, 10 |
| 11 | 1, 11 |
| 12 | 1, 2, 3, 4, 6, 12|
| 13 | 1, 13 |
| 14 | 1, 2, 7, 14 |
| 15 | 1, 3, 5, 15 |
| 16 | 1, 2, 4, 8, 16 |
| 17 | 1, 17 |
| 18 | 1, 2, 3, 6, 9, 18|
| 19 | 1, 19 |
| 20 | 1, 2, 4, 5, 10, 20|
| 21 | 1, 3, 7, 21 |
| 22 | 1, 2, 11, 22 |
| 23 | 1, 23 |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24|

Highlighting Prime Numbers:

The prime numbers from 1 to 24 are:
- 2, 3, 5, 7, 11, 13, 17, 19, 23

Final Answer:

\[
\boxed{2, 3, 5, 7, 11, 13, 17, 19, 23}
\]