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The image you've uploaded contains a series of mathematical exercises. I'll extract and solve the problems for you.

### Extracted Problems and Solutions:

1. **Problem 1:**
   - Complete the table by calculating the GCF (Greatest Common Factor) and LCM (Least Common Multiple) of the given numbers.

   | a  | b  | GCF(a, b) | LCM(a, b) |
   |----|----|-----------|-----------|
   | 24 | 36 |           |           |
   | 15 | 25 |           |           |
   | 9  | 12 |           |           |

   **Solution:**
   - For \(a = 24\), \(b = 36\):
     - GCF(24, 36) = 12
     - LCM(24, 36) = 72
   - For \(a = 15\), \(b = 25\):
     - GCF(15, 25) = 5
     - LCM(15, 25) = 75
   - For \(a = 9\), \(b = 12\):
     - GCF(9, 12) = 3
     - LCM(9, 12) = 36

   The completed table:
   | a  | b  | GCF(a, b) | LCM(a, b) |
   |----|----|-----------|-----------|
   | 24 | 36 | 12        | 72        |
   | 15 | 25 | 5         | 75        |
   | 9  | 12 | 3         | 36        |

2. **Problem 2:**
   - Find the prime factorization of each number.

   **Solution:**
   - \(20 = 2^2 \times 5\)
   - \(35 = 5 \times 7\)
   - \(42 = 2 \times 3 \times 7\)
   - \(60 = 2^2 \times 3 \times 5\)

3. **Problem 3:**
   - Evaluate whether the following numbers are prime or composite.
     - \(2\)
     - \(9\)
     - \(17\)
     - \(51\)

   **Solution:**
   - \(2\) is a prime number.
   - \(9\) is a composite number.
   - \(17\) is a prime number.
   - \(51\) is a composite number.

4. **Problem 4:**
   - Express the following as a product of prime factors:
     - \(18\)
     - \(24\)
     - \(40\)
     - \(84\)

   **Solution:**
   - \(18 = 2 \times 3^2\)
   - \(24 = 2^3 \times 3\)
   - \(40 = 2^3 \times 5\)
   - \(84 = 2^2 \times 3 \times 7\)

5. **Problem 5:**
   - Fill in the missing values in the table based on the highest common factor (HCF) and the least common multiple (LCM).

   **Solution:**
   - Without the specific table, I can’t fill in exact values. If you provide the missing values or clarify, I can assist further.

Would you like more details or explanations for any of the above problems? 

Here are some related questions you might be interested in:
1. How do you calculate the GCF and LCM of two numbers?
2. What are some real-life applications of prime factorization?
3. How can you determine if a number is prime or composite?
4. Why is the prime factorization of a number unique?
5. How does the LCM of two numbers relate to their GCF?

**Tip:** Understanding the relationship between GCF and LCM can help solve problems involving fractions, ratios, and real-world scenarios efficiently.

Explore solutions to math problems involving GCF (Greatest Common Factor), LCM (Least Common Multiple), prime factorization, and prime numbers. Understand how to calculate GCF and LCM, determine prime or composite status, and factorize numbers. Suitable for students in Grades 6-8.

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