What is the difference between GCD, GCF, and HCF?

They are the same thing with different names. GCD (Greatest Common Divisor), GCF (Greatest Common Factor), and HCF (Highest Common Factor) all refer to the largest number that divides all given numbers evenly.

How is GCD calculated?

The most efficient method is the Euclidean algorithm: repeatedly divide the larger number by the smaller and replace the larger with the remainder until the remainder is 0. The last non-zero remainder is the GCD.

What is the GCD of two prime numbers?

The GCD of two different prime numbers is always 1, since prime numbers have no common factors other than 1.

Can I find GCD of more than two numbers?

Yes! To find GCD of multiple numbers, first find GCD of the first two, then find GCD of that result with the third number, and so on. This calculator handles multiple numbers automatically.

Greatest Common Divisor (GCD) Calculator

Calculate the GCD of multiple numbers instantly. Find the greatest common divisor using Euclidean algorithm with step-by-step explanation. Perfect for fraction simplification and number theory.

Numbers

Enter numbers to calculate their GCD

Greatest Common Divisor (GCD) Calculator Tool Introduction

A powerful Greatest Common Divisor (GCD) Calculator that finds the largest number that divides all given numbers without remainder. Also known as the Greatest Common Factor (GCF) or Highest Common Factor (HCF).

Perfect for students learning number theory, teachers creating math problems, programmers implementing algorithms, and anyone working with fractions, ratios, or divisibility problems.

Our calculator uses the efficient Euclidean algorithm to compute the GCD of two or more numbers. It shows the step-by-step process and all common divisors, making it an excellent learning tool for understanding divisibility and factorization.

All calculations are performed locally in your browser for complete privacy. No data is collected or stored. Use this tool to simplify fractions, solve ratio problems, or understand number relationships.

Greatest Common Divisor (GCD) Calculator User Guide

How to Use

Enter Numbers: Input two or more positive integers (comma or space separated)
Click Calculate: Get the GCD instantly
View Steps: See the Euclidean algorithm process
Check Divisors: View all common divisors

Understanding GCD

The Greatest Common Divisor (GCD) is the largest positive integer that divides all given numbers without leaving a remainder.

Example

Find GCD of 48 and 18:

Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Divisors of 18: 1, 2, 3, 6, 9, 18
Common divisors: 1, 2, 3, 6
GCD = 6 (the greatest)

Euclidean Algorithm

GCD(48, 18):

48 = 18 × 2 + 12
18 = 12 × 1 + 6
12 = 6 × 2 + 0
GCD = 6

Key Features

Calculate GCD of 2 or more numbers
Step-by-step Euclidean algorithm
List all common divisors
Fast computation for large numbers
Support for multiple number input

Frequently Asked Questions

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