Long Division Calculator

Results

Check: 22 × 56 + 2 = 1234

Long division layout

         2 2
   ┌─────────
56 │ 1 2 3 4
     1 1 2
     ─────
       1 1 4
       1 1 2
       ─────
           2

Step by step

1. Start from the left with the first digits that make a number 56 can go into: 123. 56 goes into 123 2 times: 56 × 2 = 112. Write 2 above the line, then subtract: 123 − 112 = 11.
2. Bring down the 4. 56 goes into 114 2 times: 56 × 2 = 112. Write 2 above the line, then subtract: 114 − 112 = 2.

No digits are left to bring down, so the remainder is 2.

How to Use the Long Division Calculator

1. 1. Enter the two numbers. The dividend is the number being divided; the divisor is the number you divide by. Whole numbers and decimals both work, and either can be negative.
2. 2. Choose the kind of answer. “Quotient and remainder” gives a whole-number answer such as 22 R 2. “Decimal” keeps dividing past the decimal point and tells you when the digits end or repeat.
3. 3. Pick a layout. The bracket layout is the one used in English-speaking countries; the inline layout writes the problem as 700 : 8 = 87.5 with the subtractions underneath, as in German-speaking schools.
4. 4. Follow the steps. Under the diagram, each step is written out in words, so you can match it line for line against your own working or your homework.

How Long Division Works

Long division splits one big division into a chain of small ones, working left to right through the digits of the dividend. Every step repeats the same four moves: divide (how many times does the divisor go into the number in front of you?), multiply (that count × the divisor), subtract (take the product away to get the remainder) and bring down the next digit. The remainder with the next digit attached becomes the number for the following step: current = remainder × 10 + next digit.

The quotient digit at each step is always between 0 and 9, because if the divisor went in ten or more times, the previous step would have taken more. When the dividend runs out of digits, whatever is left over is the remainder, and it is always smaller than the divisor. That gives the relationship every division obeys: dividend = quotient × divisor + remainder.

Worked Example: 1234 ÷ 56

The calculator starts with its default numbers. The divisor 56 does not go into 1 or 12, so the first useful number is 123.

         2 2
   ┌─────────
56 │ 1 2 3 4
     1 1 2
     ─────
       1 1 4
       1 1 2
       ─────
           2

• 56 goes into 123 two times: 56 × 2 = 112, and 123 − 112 = 11.
• Bring down the 4 to make 114. 56 goes into 114 two times: 56 × 2 = 112, and 114 − 112 = 2.
• No digits are left, so the quotient is 22 and the remainder is 2.
• Check: 22 × 56 + 2 = 1232 + 2 = 1234.

Decimals, Terminating and Repeating

A remainder does not have to stop the division. Put a decimal point after the last digit, add a zero, and carry on: 1234 ÷ 56 continues as 22.0357142857… Each extra zero turns the remainder into a bigger number to divide, exactly as a digit brought down would. The process ends in one of two ways. If the remainder reaches 0, the decimal terminates. If a remainder appears that has appeared before, the digits from that point repeat forever, because the same remainder always produces the same next digit.

There are only so many possible remainders — fewer than the divisor — so a repeat is guaranteed within that many steps. A fraction in lowest terms terminates exactly when its denominator has no prime factors except 2 and 5. The calculator marks a repeating block with an overline and tells you its length.

Dividing by a Decimal, or With Negatives

Long division needs a whole-number divisor. If yours has decimals, move the decimal point the same number of places to the right in both numbers: 7.5 ÷ 0.25 becomes 750 ÷ 25, which is 30. Multiplying top and bottom by the same power of ten never changes the quotient. Negative numbers are handled by setting the signs aside: divide the absolute values, then make the answer negative if exactly one of the two numbers was negative.

Common Mistakes

• Skipping a zero in the quotient. When the divisor does not go into the current number, write 0 above the line before bringing the next digit down. Missing it turns 201 into 21.
• Misaligning columns. Each quotient digit sits above the last digit of the number it came from. The diagram keeps this alignment for you.
• Subtracting too little. If a remainder is as large as the divisor, the quotient digit was too small — raise it by one.
• Forgetting to move the point. When the divisor is a decimal, the dividend must be scaled by the same amount.

Frequently Asked Questions

How do you do long division with remainders?

Divide, multiply, subtract and bring down the next digit until none are left. What remains at the end is the remainder, written as “22 R 2” or as the mixed number 22 1/28. A remainder is always smaller than the divisor, and you can check the answer with quotient × divisor + remainder.

How do you do long division with decimals?

If the divisor is a decimal, move the point right in both numbers until the divisor is whole. Then divide as usual, and when the dividend runs out, add a decimal point and zeros and keep going. Put the decimal point in the quotient directly above the point in the dividend.

What do I do when the divisor is bigger than the first digit?

Take more digits. For 1234 ÷ 56, the divisor does not go into 1 or into 12, so you start with 123. The quotient has no digits above the ones you skipped, which is why the answer starts directly above the 3.

How can I tell whether a decimal will repeat?

Reduce the division to a fraction in lowest terms. If the denominator has any prime factor other than 2 or 5, the decimal repeats; if it only has 2s and 5s, it terminates. So 1/8 = 0.125 ends, but 1/12 = 0.08333… does not, because 12 contains a 3.

What is the bus stop method?

“Bus stop” is the nickname used in the UK for the bracket layout of long division, where the divisor sits outside the bracket and the quotient is written above it. The working is identical to the US layout; only the picture has a nickname.

Why does the calculator stop after a set number of decimal places?

Some divisions never end, so you choose how many digits to work out. The calculator stops sooner if the remainder reaches zero or a repeat appears, and it always reports the exact decimal, including the repeating block, in the results.