Long Division Calculator

How to do long division

Long division repeats the same four steps until there are no digits left:

1. Divide: how many times does the divisor go into the number you are looking at? Write that digit in the answer.
2. Multiply: multiply that digit by the divisor and write the result underneath.
3. Subtract: take it away. What is left must be smaller than the divisor.
4. Bring down the next digit next to what is left, and start again.

A way to remember the order: Does McDonald's Sell Burgers?

Worked example: 1001 ÷ 7

    143
  ┌─────
7 │ 1001
    7
    ──
    30
    28
    ──
     21
     21
     ──
      0

1. 7 doesn't go into 1, so look at 10. 7 goes into 10 once: write 1. 1 × 7 = 7, and 10 − 7 = 3.
2. Bring down the 0 to make 30. 7 goes into 30 four times: write 4. 4 × 7 = 28, and 30 − 28 = 2.
3. Bring down the 1 to make 21. 7 goes into 21 three times: write 3. 3 × 7 = 21, and 21 − 21 = 0.
4. No digits are left and nothing remains, so 1001 ÷ 7 = 143. Check: 143 × 7 = 1001.

Zeros in the answer

In 5040 ÷ 12, 12 goes into 50 four times (remainder 2), then into 24 twice (remainder 0). Bringing down the last 0 gives 0, and 12 goes into 0 zero times, so you must still write a 0 in the answer: 5040 ÷ 12 = 420, not 42. Forgetting these zeros is the most common long division mistake.

Remainders

When the digits run out and something is left, that is the remainder. 100 ÷ 7 = 14 remainder 2, often written 14 R 2. Check: 14 × 7 + 2 = 100.

The remainder can also be written as a fraction of the divisor, 14 2/7, or you can keep dividing to get a decimal: choose Decimal answer.

Decimal answers and repeating decimals

To keep going after the last digit, write a decimal point in the answer and bring down zeros. Either the remainder becomes 0 and the division ends (5 ÷ 4 = 1.25), or a remainder comes back that you have seen before. From then on the same digits repeat forever:

• 1 ÷ 3 = 0.333…, written with a bar over the 3.
• 2 ÷ 7 = 0.285714285714…, where all six digits repeat.
• 22 ÷ 7 = 3.142857…, close to π (3.14159…) but not equal to it.

Dividing by a decimal

Move the decimal point to the right until the divisor is a whole number, and move it the same number of places in the number you are dividing. 12.5 ÷ 0.25 becomes 1250 ÷ 25 = 50. Both numbers were multiplied by 100, so the answer doesn't change.

Common mistakes

• Skipping a 0 in the answer when the divisor doesn't go into the number. Every digit you bring down needs a digit in the answer.
• A remainder bigger than the divisor. If what is left after subtracting is the divisor or more, the digit you wrote was too small.
• Bringing down two digits at once. Bring down one digit per step.
• Lining up the digits wrongly. Write each answer digit straight above the last digit of the number you divided.

For teachers and parents

Press Full screen in the player to show the working large on a projector or interactive board. Copy share link saves the numbers in the link, so you can send a class straight to an example, and Print all steps prints the whole method as text. The page collects no personal information.