Greatest Common Factor Calculator
Find the Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) using multiple calculation methods
GCF Calculator
Enter at least 2 positive integers
GCF Methods & Formulas
Euclidean Algorithm
GCD(a, b) = GCD(b, a mod b)
Continue until remainder = 0
Most efficient for large numbers
Prime Factorization
1. Find prime factors of each number
2. Identify common prime factors
3. Take minimum power of each common factor
4. Multiply these together
Listing Factors
1. List all factors of each number
2. Find factors common to all numbers
3. Select the largest common factor
Best for small numbers
Key Properties
GCF(a, b) × LCM(a, b) = a × b
GCF(a, 0) = a
GCF(a, 1) = 1
GCF(a, a) = a
Common Examples
Frequently Asked Questions
The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), is the largest positive integer that divides all given numbers without leaving a remainder. For example, GCF(12, 18) = 6 because 6 is the largest number that divides both 12 and 18.
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.