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Greatest Common Factor Calculator

Find the largest common factor of several integers using exact integer arithmetic.

Your numbers

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Updates as you type
Greatest common factor
12

Calculated from your inputs · rounded for display

Number of integers3

Your calculation, step by step

No black boxes
  1. 24 = 0 × 36 + 24.
  2. 36 = 1 × 24 + 12.
  3. 24 = 2 × 12 + 0.
  4. gcd(24, 36) = 12; apply Euclid’s remainder algorithm.
  5. 12 = 0 × 60 + 12.
  6. 60 = 5 × 12 + 0.
  7. gcd(12, 60) = 12; apply Euclid’s remainder algorithm.

How to use this calculator

  1. Enter your own values in the labeled fields. Check the units and assumptions before comparing results. Only the fields needed for your selected calculation mode are shown.
  2. Your answer updates automatically. Review the calculation steps to see exactly how it was calculated.
  3. Copy, share, save, or download your result. Saved inputs stay on this device.

How the calculation works

gcd(a,b) = gcd(b, a mod b)

Signs are ignored when finding a greatest common divisor. The Euclidean remainder algorithm combines the values pairwise without converting large results to floating point. At least one entered integer must be nonzero. Review the units, period and assumptions before comparing scenarios. Displayed values are rounded, while the underlying calculation retains its available precision.

A worked example

gcd(24,36) = 12 and gcd(12,60) = 12, so the greatest common factor of 24, 36 and 60 is 12.

Reading your result

Use the main result together with its units and supporting figures. Display values are rounded; calculations keep their underlying precision. A change in inputs or assumptions can change the answer. Compare the step-by-step working with your intended use before relying on an estimate.

Frequently asked questions

What assumptions does this calculation use?

Signs are ignored when finding a greatest common divisor. The Euclidean remainder algorithm combines the values pairwise without converting large results to floating point. At least one entered integer must be nonzero.

Can I save or check a scenario?

The result includes the working and supporting values. Save and Restore keep inputs on this device; Copy, Download and Print export the result. Sharing a scenario explicitly includes the inputs in its link.

Sources & methodology

This calculator uses the mathematical identity and assumptions stated above. No current rates, prices, or external data are loaded. Conversion tools use international unit definitions.

Formula review: October 24, 2026. Read our methodology.