JLJosh Liljenquist

Arithmetic calculator

Long division calculator

Divide one integer by another and inspect the work digit by digit. The result reports the integer quotient and remainder, a decimal approximation, and an accessible ordered list of bring-down, multiply, and subtract steps.

By

Quotient and remainderDigit-by-digit stepsDecimal result

Enter known values

Enter the known values and select Calculate.

How to use this calculator

  1. Enter an integer dividend and a nonzero integer divisor.
  2. Calculate to obtain quotient and remainder.
  3. Follow each numbered bring-down and subtraction step.
  4. Use the decimal line when a remainder needs a decimal representation.

Formula and method

At each digit, divide the current partial dividend by the divisor, multiply the quotient digit by the divisor, subtract, and bring down the next digit. Dividend = divisor × quotient + remainder.

Worked example

For 789 ÷ 12, the integer quotient is 65 with remainder 9 because 12 × 65 + 9 = 789. The decimal result is 65.75.

Assumptions and result interpretation

  • Inputs are safe integers.
  • The displayed step sequence uses absolute values and applies the final sign to the quotient.
  • The remainder is nonnegative and smaller than the absolute divisor.
  • Decimal output is rounded for display when it does not terminate quickly.

Understanding the result

The identity dividend = divisor × quotient + remainder verifies the integer result. The step list shows how each quotient digit is determined rather than returning only the answer.

Common mistakes

  • Dividing by zero
  • Skipping a zero quotient digit
  • Forgetting to bring down the next digit
  • Reporting a remainder equal to or larger than the divisor

Methodology note

The calculation follows the deterministic formula shown above and runs locally in the browser without a remote calculation service.

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This deterministic utility is a calculation aid. Confirm definitions, required precision, and any course, laboratory, professional, or policy requirements separately.