🔢 GCF Calculator
Calculate greatest common factor
How to Use This Calculator
Enter Two Numbers
Input two integers to find their GCF (Greatest Common Factor).
Click Calculate GCF
Press the button to find the greatest common factor using Euclidean algorithm.
View Result
See the GCF value and calculation method.
Formula
Euclidean Algorithm: gcd(a, b) = gcd(b, a mod b)
Example 1: GCF(48, 18)
gcd(48, 18) = gcd(18, 48 mod 18) = gcd(18, 12)
gcd(18, 12) = gcd(12, 18 mod 12) = gcd(12, 6)
gcd(12, 6) = gcd(6, 12 mod 6) = gcd(6, 0)
GCF = 6
Example 2: GCF(17, 13)
Both are prime, only common factor is 1
GCF = 1 (coprime)
About GCF Calculator
The GCF Calculator finds the Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), of two numbers. GCF is the largest number that divides both numbers evenly.
When to Use This Calculator
- Simplifying Fractions: Find GCD to reduce fractions
- Mathematics: Solve GCF problems and factor polynomials
- Number Theory: Check if numbers are coprime (GCF=1)
- Education: Learn greatest common factor concepts
- Problem Solving: Find common factors efficiently
Why Use Our Calculator?
- ✅ Euclidean Algorithm: Fastest method for finding GCF
- ✅ Instant Results: Calculate GCF immediately
- ✅ Educational: Learn GCF concepts
- ✅ 100% Accurate: Precise calculations
- ✅ Completely Free: No registration required
Understanding GCF
- GCF is always ≥ 1
- If GCF = 1, numbers are coprime/relatively prime
- GCF divides both numbers evenly
- No common factor larger than GCF exists
Frequently Asked Questions
What is GCF/GCD?
Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) is the largest number that divides both numbers evenly. GCF(48, 18) = 6.
What if GCF is 1?
If GCF = 1, the numbers are coprime (relatively prime). They share no common factors except 1. Example: GCF(17, 13) = 1.
How does the Euclidean Algorithm work?
Keep replacing (a, b) with (b, a mod b) until remainder is 0. The last non-zero remainder is the GCF.