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Long Division Calculator

Solve long division problems step by step and see the quotient, remainder, decimal answer, exact fraction, and a full school-style long division layout. This calculator is built to be more student-friendly, more visual, and more educational, with guided steps, interpretation, repeating-decimal detection, and quick picks.

Background

Long division is more than just getting an answer. It helps students understand how division works through the repeatable pattern divide → multiply → subtract → bring down. This calculator is designed to show both the answer and the reasoning, so students can follow the exact process they are expected to use in class.

Enter values

What this calculator can do

Enter a dividend and divisor to see the quotient, remainder, decimal expansion, exact fraction, mixed number, and full long division workspace. It also handles decimals and can detect repeating decimal patterns.

This is the number being divided.

This is the number you divide by. It cannot be 0.

Memory trick

D = Divide M = Multiply S = Subtract B = Bring down

Options

Chips prefill and calculate immediately.

Result

No results yet. Enter values and click Calculate. A great starting example is: 157 ÷ 12

How to use this calculator

  • Step 1: Enter the dividend.
  • Step 2: Enter the divisor.
  • Step 3: Choose whether you want layout, steps, decimals, and exact fraction output.
  • Step 4: Click Calculate to see the full long division process.

For decimal division, the calculator rewrites the problem as an equivalent whole-number division so the workspace is easier to read.

How this calculator works

  • It rewrites decimal division as an equivalent whole-number division when needed.
  • It performs long division one digit at a time: divide, multiply, subtract, and bring down.
  • If there is a remainder, it can continue into decimal places.
  • If the same remainder appears again, the decimal repeats.
  • It also simplifies the exact fraction form of the answer.

Formula & Relationship Used

Main division relationship: Dividend = Divisor × Quotient + Remainder

Remainder rule: 0 ≤ Remainder < Divisor

Equivalent decimal scaling: multiplying both numbers by the same power of 10 does not change the quotient.

Example Problems & Step-by-Step Solutions

Example 1 — Whole-number division

157 ÷ 12

  1. 12 goes into 15 one time.
  2. Write 1 in the quotient.
  3. Subtract 12 from 15 to get 3.
  4. Bring down the 7 to make 37.
  5. 12 goes into 37 three times.
  6. Subtract 36 from 37 to get remainder 1.

Example 2 — Division that ends in a decimal

625 ÷ 4

  1. 4 goes into 6 one time.
  2. Continue the long division.
  3. The quotient is 156 with remainder 1.
  4. Continue past the decimal point to get 156.25.

Example 3 — Repeating decimal

1 ÷ 3

  1. 3 does not go into 1, so the whole-number quotient is 0.
  2. Add a decimal point and continue.
  3. Bring down 0 to make 10.
  4. 3 goes into 10 three times with remainder 1 again.
  5. Because the same remainder repeats, the decimal repeats: 0.333...

Frequently Asked Questions

Q: What is the difference between quotient and remainder?

The quotient is the main answer to the division problem. The remainder is what is left over after dividing as evenly as possible.

Q: Why does a decimal repeat?

A decimal repeats when the same remainder appears again during long division. At that point, the digit pattern starts cycling.

Q: Why does the calculator rewrite decimal division?

Multiplying both the dividend and divisor by the same power of 10 creates an equivalent division problem that is easier to show in long-division form.

Q: Can this calculator handle negative numbers?

Yes. The sign of the final answer depends on the signs of the inputs: same signs give a positive result, and different signs give a negative result.