Whether you’re simplifying fractions, working with ratios, or solving math problems, knowing how to calculate the Greatest Common Factor (GCF) is super helpful.
Let’s break it down so it’s easy to understand—even if math isn’t your thing.
Table of Contents
🙋 What Is GCF?
GCF (Greatest Common Factor) is the largest number that can divide two or more numbers evenly—with no leftovers.
Think of it as the biggest number that two or more numbers have in common as a factor.
✏️ Example: What’s the GCF of 12 and 18?
Let’s find all the numbers that divide evenly into each:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 18 = 1, 2, 3, 6, 9, 18
👉 The largest number they both share is 6
✅ So, GCF = 6
🧮 Three Easy Ways to Find the GCF
1. List the Factors
Step 1: Write down all the factors of each number
Step 2: Find the biggest one they both share
Works best for small numbers
2. Prime Factorization
Break each number down into its prime factors (numbers that can’t be divided further except by 1 and itself)
Example:
- 12 = 2 × 2 × 3
- 18 = 2 × 3 × 3
Shared prime factors: 2 × 3 = 6
✅ So, GCF = 6
3. Division Method (a.k.a. Euclidean Algorithm)
For bigger numbers, this method is fast!
Step 1: Divide the larger number by the smaller
Step 2: Take the remainder and divide the smaller number by it
Step 3: Keep repeating until the remainder is 0
The last divisor is the GCF
Example: GCF of 48 and 18
- 48 ÷ 18 = 2 remainder 12
- 18 ÷ 12 = 1 remainder 6
- 12 ÷ 6 = 2 remainder 0
✅ GCF = 6
📘 When Do You Use GCF?
- 📐 Simplifying fractions (e.g., 12/18 → divide top and bottom by GCF = 2/3)
- 🎂 Dividing things evenly (like splitting items into equal groups)
- 🧩 Working with ratios or scaling numbers
✅ Quick Recap
| Method | Best For | How It Works |
|---|---|---|
| List the Factors | Small numbers | Write all factors, find the largest shared one |
| Prime Factorization | Medium-sized numbers | Break numbers into prime factors |
| Division Method | Bigger numbers | Use remainders until you get zero |