CalculatorCheckSearch

Math Calculators

GCD / HCF Calculator

Find the GCD or HCF with Euclidean steps and Bézout coefficients for two values.

Find the greatest integer that divides every entered value.

Calculate with the GCD / HCF Calculator

Enter the values below. Invalid mathematical operations are explained before a result is shown.

Separate values with commas, spaces, or new lines.

How to use the GCD / HCF Calculator

  1. Choose a calculation mode when one is available.
  2. Enter the required values using the examples and field notes as a guide.
  3. Select Calculate or press Enter.
  4. Review the primary result, supporting values, and working.

Worked example

48 = 18×2 + 12; 18 = 12×1 + 6; 12 = 6×2, so GCD = 6.

Assumptions

The calculator uses real-number arithmetic unless complex square or quadratic roots are explicitly shown. Decimal displays can be rounded while calculations retain normal browser numeric precision.

Limitations

  • The all-zero list has no finite greatest common divisor here.
  • Bézout coefficients are shown only for two integers.

Frequently asked questions

Does the GCD / HCF Calculator accept decimals and negative values?

It accepts them wherever the selected operation permits. Invalid domains are identified before a result is shown.

How are decimal results rounded?

Calculations retain JavaScript numeric precision and display a readable number of significant digits. A displayed decimal may therefore be rounded.

Are entries stored?

No. The calculation runs in your browser and this page does not store the values you enter.

Related calculators