Long Division Calculator

This long division calculator helps you divide whole numbers and decimals while showing the work step by step.

How to Calculate a Long Division Problem?

Long division is a way to divide a large number by working from left to right. The number being divided is called the dividend, and the number you divide by is called the divisor. For example, in 200 ÷ 13, the dividend is 200 and the divisor is 13.

In written long division, place the dividend inside the division bracket and the divisor on the outside. Then follow a repeating pattern: divide, multiply, subtract, and bring down the next digit.

Step 1: Start with the first digit

Look at the first digit of the dividend. In this example, the first digit is 2. Since 13 cannot go into 2, you move to the next digit and use 20 instead. Some teachers write a 0 above the first digit, while others simply begin the quotient above the digit where division starts.

Step 2: Divide the first usable number

Now ask how many times 13 fits into 20. It fits 1 time. Write 1 in the quotient, multiply 13 × 1 = 13, and place 13 below 20.

Step 3: Subtract and bring down

Subtract 13 from 20 to get 7. Then bring down the next digit from the dividend, which is 0. This makes the new working number 70.

Step 4: Repeat the same process

Next, find how many times 13 fits into 70. It fits 5 times because 13 × 5 = 65. Write 5 in the quotient, subtract 65 from 70, and the remainder is 5.

At this point, the whole-number answer is:

200 ÷ 13 = 15 remainder 5

Step 5: Continue into decimals if needed

If you want a decimal answer instead of stopping at the remainder, place a decimal point after the quotient. Add a zero after the remainder and continue the same divide, multiply, subtract, and bring-down pattern.

For 200 ÷ 13, the decimal continues:

200 ÷ 13 = 15.384615384615...

This decimal repeats, so depending on your purpose, you may leave the answer as a quotient with a remainder, as a mixed number, or as a decimal rounded to a certain number of places.

What This Calculator Shows

• Quotient: the main division answer.
• Remainder: the amount left after division when the answer is not exact.
• Decimal result: the quotient written as a decimal.
• Long division steps: each divide, multiply, subtract, and bring-down step.
• Decimal-place option: continue the work into a selected number of decimal places.

How to Use the Long Division Calculator

1. Enter the divisor in the left input box.
2. Enter the dividend in the right input box.
3. Click Calculate to see the result and steps.
4. If you want decimal steps, check the decimal-place option and enter how many decimal places to show.
5. Click Clear to reset the calculator.

FAQ

What is the dividend?

The dividend is the number being divided. In 200 ÷ 13, the dividend is 200.

What is the divisor?

The divisor is the number you divide by. In 200 ÷ 13, the divisor is 13.

What does the remainder mean?

The remainder is what is left after the divisor has gone into the dividend as many whole times as possible. For example, 200 ÷ 13 gives a quotient of 15 with a remainder of 5.

Can long division produce decimals?

Yes. If there is a remainder, you can add a decimal point and continue the division by bringing down zeros.

Why do some decimal answers repeat?

A decimal repeats when the division never ends and the same remainder pattern appears again. In that case, the decimal can be rounded or written using repeating-decimal notation.

References

For broader information about mathematics education and student assessment, you may visit these official resources:

• The Nation's Report Card: Mathematics - National Center for Education Statistics
• National Center for Education Statistics
• U.S. Department of Education

These links are provided as general educational references. They do not imply endorsement of this calculator.