GCF Calculator
Calculate Greatest Common Factor (GCF) of two numbers.
Numbers
Results
GCF / GCD
6
Greatest Common Factor
Common Factors
1, 2, 3, 6
All Factors:
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
18: 1, 2, 3, 6, 9, 18
About This Calculator
The GCF (Greatest Common Factor) Calculator helps you find the greatest common factor, also known as the greatest common divisor (GCD), of two numbers. The GCF is the largest positive integer that divides both numbers without leaving a remainder.
The calculator uses the Euclidean algorithm, an efficient method to find the GCF. It also shows all factors of both numbers and identifies the common factors. The GCF is useful for simplifying fractions, reducing ratios, and solving various mathematical problems.
Formula & Calculation Method
GCF/GCD Calculation:
Euclidean Algorithm:
GCD(a, b) = GCD(b, a mod b)
Continue until remainder is 0
The last non-zero remainder is the GCD
Example:
GCD(48, 18):
48 = 18 × 2 + 12
18 = 12 × 1 + 6
12 = 6 × 2 + 0
GCD = 6
The Euclidean algorithm is an efficient method to find the GCF. It repeatedly applies the division algorithm: divide the larger number by the smaller, then replace the larger with the smaller and the smaller with the remainder, until the remainder is 0.
How to Use This Calculator
- Enter Number 1: Input the first number.
- Enter Number 2: Input the second number.
- View Results: See the GCF, all factors, and common factors.
- Use GCF: Use the GCF to simplify fractions, reduce ratios, or find common divisors.
Frequently Asked Questions
What is GCF?
GCF (Greatest Common Factor), also called GCD (Greatest Common Divisor), is the largest positive integer that divides both numbers without leaving a remainder. For example, GCF(12, 18) = 6 because 6 is the largest number that divides both 12 and 18.
How is GCF different from LCM?
GCF is the largest number that divides into both numbers, while LCM is the smallest number that both numbers divide into. They are related: GCF(a, b) × LCM(a, b) = a × b.
When is GCF used?
GCF is commonly used for: simplifying fractions (divide numerator and denominator by GCF), reducing ratios to simplest form, finding common divisors, solving problems involving divisibility, and in the Euclidean algorithm for modular arithmetic.
What is the Euclidean algorithm?
The Euclidean algorithm is an efficient method to find the GCF. It repeatedly divides the larger number by the smaller, replacing numbers with remainders, until the remainder is 0. The last non-zero remainder is the GCF.
Calculator by
NumCalculators Editorial Team
Multi-disciplinary Expert Team