Algebra & Math Tool
Euclid's Algorithm (GCD)
Find the Greatest Common Divisor (GCD) using the step-by-step Euclidean algorithm.
Greatest Common Divisor
6
Walkthrough Steps
48 = (2 × 18) + 12
18 = (1 × 12) + 6
12 = (2 × 6) + 0
GCD is 6
Σ The Formula
gcd(a, b) = gcd(b, a mod b)
Real World Examples
Standard Pair
GCD of 48 and 18 is 6.
Large Numbers
Check the GCD of 1071 and 462 through iterative subtraction/division.
# About This Calculator
Euclid's Algorithm is an ancient and efficient method for computing the greatest common divisor (GCD) of two integers—the largest number that divides them both without a remainder.
It works on the principle that the GCD of two numbers also divides their difference. This tool performs the division version of the algorithm, which is much faster than repeated subtraction.
How To Use
- Enter the **First Number (A)**.
- Enter the **Second Number (B)**.
- The **GCD** is calculated instantly.
- Scroll down to see the **Detailed Steps** showing each division and remainder.
Frequently Asked Questions
What is a GCD used for?+
GCD is used to simplify fractions and find common denominators. It's also a building block in advanced cryptography.
What if the GCD is 1?+
If the GCD is 1, the two numbers are said to be 'relatively prime' or 'coprime'.
Is Euclid's Algorithm (GCD) free to use?+
Yes, Euclid's Algorithm (GCD) on Matheric is completely free to use. We believe in accessible education and utility for everyone.
How accurate is Euclid's Algorithm (GCD)?+
We use standard mathematical formulas and high-precision computing algorithms to ensure results for Euclid's Algorithm (GCD) are accurate for academic and professional use.
Can I use Euclid's Algorithm (GCD) on my phone?+
Yes! Euclid's Algorithm (GCD) is fully responsive and optimized for all devices, including smartphones, tablets, and desktops.
Do you save my data?+
No. We prioritize your privacy. All calculations are performed in your browser or temporarily processed, and we do not store your personal input data.