HCF / GCD Calculator
Find the Greatest Common Divisor (also known as HCF) of multiple numbers.
Separate values with commas or spaces.
Σ The Formula
Real World Examples
# About This Calculator
The Greatest Common Divisor (GCD), also known as the Highest Common Factor (HCF) or Greatest Common Factor (GCF), is the largest positive integer that divides each of the given integers without leaving a remainder. It's a fundamental concept in number theory with practical applications.
GCF is essential for simplifying fractions (divide numerator and denominator by their GCF), solving problems involving equal grouping or distribution, finding the largest square tiles that fit a rectangular space, and understanding number relationships. It's also crucial in cryptography and computer science algorithms.
The Euclidean algorithm efficiently finds GCF: GCF(a,b) = GCF(b, a mod b), repeating until remainder is 0. For multiple numbers, find GCF pairwise. Alternatively, list all factors and find the largest common one, or use prime factorization (multiply common prime factors with lowest powers).
This calculator handles multiple numbers simultaneously, shows step-by-step factor listings, and identifies all common factors. Perfect for homework, fraction simplification, or any problem requiring the largest common divisor.
How To Use
- Enter numbers separated by commas or spaces (e.g., "12, 18, 30").
- Click Calculate GCF.
- The tool will show you the common factors and the greatest one.
Frequently Asked Questions
Is GCD the same as HCF?+
How do I use GCF to simplify fractions?+
What's the GCF of two prime numbers?+
Can GCF be larger than one of the numbers?+
How is GCF related to LCM?+
Can GCF be 1?+
About
The Greatest Common Divisor (GCD), also known as the Highest Common Factor (HCF) or Greatest Common Factor (GCF), is the largest positive integer that divides each of the given integers without leaving a remainder. It's a fundamental concept in number theory with practical applications.
GCF is essential for simplifying fractions (divide numerator and denominator by their GCF), solving problems involving equal grouping or distribution, finding the largest square tiles that fit a rectangular space, and understanding number relationships. It's also crucial in cryptography and computer science algorithms.
The Euclidean algorithm efficiently finds GCF: GCF(a,b) = GCF(b, a mod b), repeating until remainder is 0. For multiple numbers, find GCF pairwise. Alternatively, list all factors and find the largest common one, or use prime factorization (multiply common prime factors with lowest powers).
This calculator handles multiple numbers simultaneously, shows step-by-step factor listings, and identifies all common factors. Perfect for homework, fraction simplification, or any problem requiring the largest common divisor.