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Euclidean Algorithm Calculator.

Find the greatest common divisor and show each Euclidean division step.

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Set your values

Results update as you type.

Greatest common divisor: 21

Greatest common divisor

0.000000
Euclidean steps: 252 = 2 × 105 + 42; 105 = 2 × 42 + 21; 42 = 2 × 21 + 0

Euclidean steps

252 = 2 × 105 + 42; 105 = 2 × 42 + 21; 42 = 2 × 21 + 0

Results update automatically as you type.

Use Cases

Simplify fractions

Find the GCD of the numerator and denominator to reduce a fraction to its simplest form.

Example: For 24/36, GCD is 12, so the fraction simplifies to 2/3.

Solve number theory problems

Use the Euclidean algorithm to find the GCD in various math problems, such as finding common divisors or preparing for modular arithmetic.

Example: Find GCD(48, 18) = 6.

Frequently Asked Questions

What does the Euclidean Algorithm Calculator do?
It finds the greatest common divisor (GCD) of two integers you enter. It shows each step of the Euclidean division process, making it easy to follow how the GCD is derived.
How do I use the calculator?
Enter two integers in the fields labeled 'First integer' and 'Second integer'. The calculator will compute their GCD and display the step-by-step Euclidean divisions.
Can I use negative numbers?
The Euclidean algorithm typically works with positive integers, but the GCD of two integers is always positive. If you enter negative numbers, the calculator will likely take their absolute values to compute the GCD.

Tips & Common Mistakes

Tips

  • Enter positive integers for best results; the calculator will handle negatives by using absolute values.
  • Use the step-by-step display to understand how the Euclidean algorithm works.
  • Check your inputs for typos – the GCD is sensitive to the numbers you enter.
  • Use the GCD to simplify ratios or fractions in your math homework.

Common Mistakes to Avoid

  • Entering zero as one of the integers – the GCD of 0 and a non-zero number is the absolute value of the non-zero number, but the algorithm may not show steps.
  • Expecting the calculator to show steps for non-integer inputs – it only works with integers.
  • Confusing the GCD with the least common multiple (LCM) – this calculator only finds the GCD.

Last updated: August 13, 2026