Long division calculator with steps, remainders and decimals

This long division calculator sets out a division the written way and builds it up one step at a time, so you can follow or check every line. Type the number being divided and the number you are dividing by, then choose to finish with a remainder or carry on into decimals. It gives the answer as a remainder, a decimal (with recurring digits marked by dots), a fraction and a mixed number.

It opens on 1000 ÷ 7. Change the numbers, or open the full long division calculator over this page.

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Long Division Calculator

Divide step by step, with remainders and decimals

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How to use the long division calculator

1. Type the dividend (the number being divided) in Number being divided, and the divisor in Divided by. Decimals and negative numbers are fine.
2. Under Finish with, choose Remainder to stop at a whole number answer with a remainder, or Decimals to keep dividing after the decimal point.
3. Read the answers at the top: the remainder form, the decimal, the fraction and the mixed number, plus how many digits repeat if the decimal recurs.
4. The written layout opens finished. Use the arrows above it to go back to the start and step forward one digit at a time. A caption under the arrows says what happens at each step.
5. The working beside it lists each step in words: how many times the divisor goes, the multiplication and the subtraction.
6. To practise, press Random problem in the Practice section for a three-digit number divided by a number from 3 to 12.

It works exactly, with no rounding, for up to 30 digits in total and up to 15 digits in the divisor. Recurring decimals are written out for up to 24 decimal places, and the calculator keeps looking for the repeat well beyond that.

How to do long division: the steps

Write the divisor outside the bracket and the dividend inside. Then work from left to right, repeating four steps for each digit:

1. Divide: how many times does the divisor go into the number you are looking at? Write that digit above.
2. Multiply: that digit times the divisor. Write it underneath.
3. Subtract: take it away to get the remainder. It must be smaller than the divisor.
4. Bring down: the next digit of the dividend, next to the remainder, and start again.

Divide, multiply, subtract, bring down. When there are no digits left to bring down, whatever is left is the remainder. To carry on into decimals, put a decimal point in the answer, write a 0 after the dividend's decimal point and bring that down instead.

Worked examples you can check in the calculator

Example 1: dividing by one digit

Work out 7452 ÷ 6.

Reading the digits from the top: 7452 ÷ 6 = 1242, with no remainder.

Example 2: long division with a remainder

Work out 2359 ÷ 8, and choose Remainder in the calculator. 8 doesn't go into 2, so start with 23.

• 8 goes into 23 twice: 2 × 8 = 16, and 23 − 16 = 7. Bring down 5 to make 75.
• 8 goes into 75 nine times: 9 × 8 = 72, and 75 − 72 = 3. Bring down 9 to make 39.
• 8 goes into 39 four times: 4 × 8 = 32, and 39 − 32 = 7. There is nothing left to bring down.

So 2359 ÷ 8 = 294 r 7. The remainder 7 is still to be shared among 8, so as a mixed number it is 294 7/8, and as a decimal it is 294.875. The calculator shows all three. Check: 294 × 8 + 7 = 2359.

Example 3: long division with a 2 digit divisor

Work out 8736 ÷ 24. With a two-digit divisor, it helps to jot down a few multiples first: 24, 48, 72, 96, 120, 144, 168.

• 24 doesn't go into 8, so look at 87. It goes 3 times: 3 × 24 = 72, and 87 − 72 = 15. Bring down 3 to make 153.
• 24 goes into 153 six times: 6 × 24 = 144, and 153 − 144 = 9. Bring down 6 to make 96.
• 24 goes into 96 four times exactly: 4 × 24 = 96, remainder 0.

So 8736 ÷ 24 = 364.

Example 4: long division with a decimal answer

Work out 47 ÷ 8 as a decimal. 8 goes into 47 five times with 7 left. Write 47 as 47.000, put the point in the answer, and keep going:

• Bring down 0 to make 70: 8 goes 8 times (64), leaving 6.
• Bring down 0 to make 60: 8 goes 7 times (56), leaving 4.
• Bring down 0 to make 40: 8 goes 5 times exactly.

So 47 ÷ 8 = 5.875. It ends because the remainder reached 0.

Example 5: a recurring (repeating) decimal

1000 ÷ 7, the calculator's opening sum, never ends. The whole number part is 142 r 6, and carrying on gives 142.857142857... The remainders after the point go 4, 5, 1, 3, 2, 6, and once 6 comes up again everything repeats. The calculator spots that repeated remainder, stops, and marks the repeating block 857142 with a dot over its first and last digits. As a fraction the answer is 1000/7, or 142 6/7.

Dividing by 7 gives at most 6 repeating digits, because there are only 6 possible non-zero remainders. In general, dividing by n repeats within n − 1 digits.

Example 6: dividing by a decimal

Work out 7.65 ÷ 0.15. Long division needs a whole number divisor, so move both decimal points two places to the right: 7.65 ÷ 0.15 = 765 ÷ 15. That doesn't change the answer, because both numbers have been multiplied by 100. Then 15 goes into 76 five times (75) with 1 left, bring down 5 to make 15, and 15 goes once. So the answer is 51. The calculator does the same shift and shows it as its first step.

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Remainders: what the answer means

The dividend is the number being divided, the divisor is the number you divide by, the quotient is the answer, and the remainder is what is left over. They always fit together like this:

A word problem decides how to use the remainder. 2359 people sharing minibuses that seat 8 need 295 buses, because the last 7 still need a seat: round up. 2359 sweets packed in bags of 8 make 294 full bags: round down. Sharing £2359 (or $2359) between 8 people gives £294.875 each, which is a decimal. The national curriculum in England asks year 6 pupils to interpret remainders as whole numbers, fractions or by rounding, depending on the context.

Long division and bus stop division

In the UK, short division is often called the bus stop method because of the shape of the bracket. Short division does the multiplying and subtracting in your head and writes each remainder as a small digit beside the next one. Long division writes every step out underneath, which is easier to check when the divisor has two or more digits. The steps are the same, and the calculator sets out the long form. In England, short division by one digit comes in year 5 and long division by two digits in year 6. In the US, the Common Core standards expect students to divide multi-digit numbers fluently with the standard algorithm by grade 6.

Common mistakes

• Missing a zero in the answer. If the divisor doesn't go into the number after you bring a digit down, write 0 in the answer before bringing down the next digit. Skipping it shifts every digit after it.
• A remainder that's too big. If you subtract and get a number bigger than or equal to the divisor, it went one more time than you wrote.
• Bringing down two digits at once. Bring down one digit per step.
• Forgetting the decimal point. Put it in the answer directly above the dividend's point before you bring down the first decimal digit.
• Moving only one point when dividing by a decimal. Move both by the same number of places.
• Not checking. Multiply the answer by the divisor and add the remainder: you should get the dividend back.

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