Understanding the Greatest Common Factor (GCF) Using the Division Method
The greatest common factor (GCF) of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder. The division method is an effective way to find the GCF.

Steps to Find GCF Using the Division Method
1. **Identify the Numbers**
- Begin with the two numbers for which you want to find the GCF.
2. **Divide the Larger Number by the Smaller Number**
- Perform the division of the larger number by the smaller number.
- Record the quotient and the remainder.
3. **Repeat the Process**
- Replace the larger number with the smaller number and the smaller number with the remainder obtained from the previous division.
- Continue dividing until the remainder is zero.
4. **Identify the GCF**
- The last non-zero remainder is the GCF of the two numbers.

Example of the Division Method
- Suppose we need to find the GCF of 48 and 18.
- **First Division:**
48 ÷ 18 = 2 (remainder 12)
- **Second Division:**
18 ÷ 12 = 1 (remainder 6)
- **Third Division:**
12 ÷ 6 = 2 (remainder 0)
- The last non-zero remainder is 6. Thus, GCF(48, 18) = 6.

Benefits of the Division Method
- **Efficiency:** This method is systematic and reduces large numbers quickly.
- **Clarity:** It provides a clear step-by-step approach, making it easy to follow.
- **Applicability:** Can be used for any pair of integers, regardless of size.
By applying the division method, you can efficiently determine the GCF of any set of numbers, which is particularly useful in various mathematical applications, including simplifying fractions and solving problems in number theory.