CALCULATE WITH CONFIDENCE

Arithmetic Operations

Quotient & Remainder Calculator

Find the unique whole-number quotient and remainder for a non-negative dividend and positive divisor.

Exact arithmetic

Divide two non-negative integers

Up to 2,000 digits

Integer division result

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Enter valid values to see the result.

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Quick guide

How to use this calculator

  1. Enter a non-negative integer dividend.
  2. Enter a positive integer divisor.
  3. Read the quotient and remainder.
  4. Use the displayed identity to verify the answer.

Calculation method

The quotient–remainder identity

For a non-negative integer dividend and positive integer divisor, the calculator finds unique integers q and r such that dividend = divisor × q + r and 0 ≤ r < divisor.

Every result is computed with arbitrary-size integers, so large accepted values are not rounded.

Worked example

Divide 125 by 8

Eight fits into 125 fifteen times, leaving five. Multiplying back confirms the result.

125 = 8 × 15 + 5

Supported inputs

Precision and limits

Integers only

Decimals and negative values are outside this calculator's domain.

Positive divisor

The divisor must be greater than zero.

Large exact values

Each integer may contain up to 2,000 digits.

Automatic check

The result includes the identity that reconstructs the dividend.