Loading...
Free online GCF calculator to find the greatest common factor of 2, 3, or more numbers instantly. Calculate GCF with step-by-step solutions using prime factorization and Euclidean algorithm.
The Greatest Common Factor (GCF) of two or more numbers is the largest positive integer that divides all the given numbers evenly without leaving a remainder. It's also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF).
For example, the GCF of 12 and 18 is 6 because:
GCF is essential in mathematics for simplifying fractions, dividing things into equal groups, solving problems involving ratios, and various real-world applications in construction, cooking, and resource distribution.
Find the prime factors of each number and multiply the lowest powers of all common prime factors.
Repeatedly divide and take remainders until reaching zero. The last non-zero remainder is the GCF.
List all factors of each number and find the largest common one.
Divide the numbers by common prime factors until no common factors remain, then multiply all common divisors.
For any two numbers a and b:
Example: GCF(12, 18) × LCM(12, 18) = 6 × 36 = 216 = 12 × 18 ✓
Reducing fractions to lowest terms by dividing numerator and denominator by their GCF. Essential in cooking and measurements.
Dividing items into equal groups without leftovers. Distributing supplies, organizing teams, or sharing resources.
Finding the largest size that divides evenly into different lengths. Cutting wood, fabric, or other materials efficiently.
Finding the largest tile size that fits perfectly in different dimensions without cutting or waste.
Creating repeating patterns with different element sizes. Grid layouts and symmetrical designs.
Determining optimal package sizes for different quantities. Organizing items in boxes or containers efficiently.
Find least common multiple
Simplify and calculate fractions
Find all factors of numbers
Advanced math operations
Calculate percentages easily
Simplify and calculate ratios
Calculate powers and exponents
Square root, cube root calculator
Comprehensive lessons on greatest common factor with practice problems and video tutorials
Visit Khan Academy →Mathematical definitions and properties of greatest common divisor with advanced concepts
Visit MathWorld →Easy-to-understand explanations with examples, interactive tools, and visual demonstrations
Visit Math is Fun →Detailed tutorials on finding GCF and its relationship with LCM, with step-by-step examples
Visit Purplemath →Unlike basic calculators limited to 2 numbers, we support GCF calculation for 2, 3, 4, or more numbers simultaneously with accurate results.
See detailed solutions using both prime factorization and Euclidean algorithm methods to understand different approaches.
Complete breakdown of the calculation process with prime factorization for each number, helping students learn and verify their work.
Add or remove numbers easily with our flexible interface. No fixed limit on how many numbers you can calculate at once.
One-click access to common GCF problems for faster learning and testing with preset values like GCF(12,18) and GCF(24,36).
12+ detailed FAQs covering all aspects of GCF, multiple calculation methods, and real-world applications to deepen understanding.
Clear explanation of the difference and mathematical relationship between GCF and LCM with visual examples and formulas.
Built-in reference table of common GCF calculations for quick lookup, verification, and homework help.
Practical examples showing how GCF is used in everyday life - from simplifying fractions to dividing materials and organizing groups.
Detailed explanation of the efficient Euclidean algorithm method with step-by-step examples for advanced learners.
Works perfectly on all devices - smartphones, tablets, and desktops with an intuitive touch-friendly interface.
No ads, no sign-up, no limitations. Completely free with unlimited calculations for students, teachers, and professionals.