To find the Greatest Common Factor (GCF) of a number (let's denote it as \( a \)) over 12, we need to know the value of \( a \). The GCF of two numbers is the largest positive integer that divides both of them without leaving a remainder.

### General Steps to Find the GCF:

1. **List the factors** of each number.
2. **Identify the common factors** between the two numbers.
3. The **greatest common factor** among them is the GCF.

### Example:

If \( a = 36 \), the steps would be:

1. **Factors of 36:** \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
2. **Factors of 12:** \( 1, 2, 3, 4, 6, 12 \)
3. **Common factors:** \( 1, 2, 3, 4, 6, 12 \)
4. **GCF:** \( 12 \)

So, the GCF of 36 and 12 is 12.

### Without a specific value for \( a \), it's impossible to calculate the exact GCF. However, you can apply this method for any given number.

Would you like to provide a specific value for \( a \) or any additional details? 

Here are some follow-up questions:

1. What is the GCF of 48 and 12?
2. How would you find the GCF of 24 and 60?
3. What is the GCF of 15 and 12?
4. How does the GCF relate to the Least Common Multiple (LCM)?
5. Can you explain how the Euclidean algorithm helps in finding the GCF?

**Tip:** The GCF is particularly useful in simplifying fractions and solving problems involving ratios.

Discover the method to find the Greatest Common Factor (GCF) of a number over 12 using factorization. Understand key concepts in number theory and apply the GCF formula effectively. Suitable for students in Grades 6-8.

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