NUMBER LAB · EXPLORE WITH CONFIDENCE

Modular Arithmetic Workbench

Calculate exact modular sums, products, powers, inverses and division, with normalized residues and verification steps.

Worked examplesBrowser processingTXT · CSV · JSON

Explore the example, or adjust the inputs. Save a project to keep your settings.

A useful starting point

The inverse of 3 modulo 11 is 4 because 3 × 4 leaves remainder 1. Therefore 8 ÷ 3 modulo 11 is 10.

Scope and limits

Signed integers up to 100 digits; modulus at least 2. Powers require a nonnegative exponent. Inverse and division require coprime operands.

Calculations run in your browser. Projects are saved only when you download them. Website advertising and analytics follow the privacy and consent settings. Import large integer CSV columns as text in spreadsheets to preserve their digits.

Using Modular Arithmetic Workbench

Calculate exact modular sums, products, powers, inverses and division, with normalized residues and verification steps.

Choose a worked example or enter your own values in the labeled controls.
Adjust the available options. Results refresh when you leave a field or choose an option.
Review the result summary, interpretation and calculation table. Check any explicit limits or assumptions.
Copy the text or download TXT, CSV or JSON. Save a project to reopen the same inputs later.

Example

The inverse of 3 modulo 11 is 4 because 3 × 4 leaves remainder 1. Therefore 8 ÷ 3 modulo 11 is 10.

Questions & answers

Why can modular division fail?

A divisor has an inverse only when its GCD with the modulus is 1. The tool reports that GCD when no inverse exists.

Can I use this for encryption?

No. It is an educational arithmetic tool, not a cryptographic system. It does not provide constant-time execution or key security.

Can I save and reopen my settings?

Yes. Save project downloads a JSON file for this tool. Open project restores it; undo and redo work during the current session.

Does the table contain every result?

The table is paginated in groups of 50. Downloads contain all listed rows. The partition tool intentionally caps its example listing while reporting the full exact count.