GCF Calculator

Calculate the Greatest Common Factor (GCF) of two or more numbers.

Loading...

Features

Smart Chip Input

Add multiple numbers easily with a modern, interactive input system.

Instant Calculation

Utilizes the Euclidean algorithm for immediate and accurate results, even with large numbers.

Prime Factorization

Visual breakdown of factors (e.g., 12 = 2² × 3¹) to show exactly how the GCF is derived.

Educational Insights

Learn the method behind the math with clear explanations and formulas.

One-Click Copy

Instantly copy the result to your clipboard for use in other applications.

About GCF Calculator

The GCF Calculator (Greatest Common Factor) is a precise mathematical tool designed to find the largest positive integer that divides two or more numbers without a remainder. It employs the robust Euclidean algorithm for instant calculations and provides a detailed Prime Factorization breakdown for educational purposes. Formula: GCF(a, b) = GCD(a, b) Using Euclidean algorithm: GCD(a, b) = GCD(b, a mod b) Alternatively, using Least Common Multiple: GCF(a, b) = |a × b| / LCM(a, b) This tool is essential for simplifying fractions, solving ratio problems, and understanding number theory concepts.

How to Use GCF Calculator

  • 1
    Enter Numbers

    Type a number and press Enter or click the Add button. You can add multiple numbers.

  • 2
    Review Inputs

    Verify your numbers in the chip list. Remove any incorrect entries with the delete icon.

  • 3
    Calculate GCF

    Click the Calculate GCF button to process the numbers.

  • 4
    View Analysis

    See the final GCF result and the detailed prime factorization breakdown below it.

Frequently Asked Questions

Yes, Greatest Common Factor (GCF) and Greatest Common Divisor (GCD) are the same thing.
The GCF of distinct prime numbers is always 1.
No, the GCF must be less than or equal to the smallest number in the set.
The GCF of 1 and any integer 'n' is always 1, as 1 is the only factor of 1.
Two numbers are Coprime (or relatively prime) if their GCF is 1. For example, 8 and 9 are coprime.
If you have 12 apples and 8 oranges and want to make identical fruit baskets with no leftovers, GCF(12,8)=4 tells you can make 4 baskets.