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Long Division Calculator

Long division, worked out the way it is done on paper. Divide, multiply, subtract, bring down, with the remainder, the decimal, and the digits that repeat.

Enter the dividend and the divisor to see the long division worked out.

Exact calculation. Given your inputs, this is the answer — no estimation involved.

How this calculator works

Long division breaks a big division into small ones. Working left to right through the dividend, each step divides, multiplies, subtracts, and brings down the next digit, until there are no digits left. The number left over is the remainder.

Enter the number being divided (the dividend) and the number you are dividing by (the divisor). With whole numbers you get the answer with a remainder, such as 13 R 1. The calculator also carries on past the decimal point, bringing down zeros, to give the decimal answer.

If the divisor has a decimal point, the first step moves it: 4.5 ÷ 1.5 becomes 45 ÷ 15, which has the same answer. A dividend with decimals is divided as normal, with the decimal point written in the answer directly above the one in the dividend.

Every step uses exact whole-number arithmetic, so nothing is rounded. When a remainder comes around a second time, the digits from that point repeat forever. That is how the calculator knows 1 ÷ 7 = 0.142857… repeats in a block of six, rather than guessing from a rounded decimal.

The formula

Exactly what happens to your numbers, step by step.

Each step

divide → multiply → subtract
→ bring down the next digit

Checking the answer

quotient × divisor + remainder = dividend

Dividing by a decimal

move the point right in both numbers
until the divisor is whole

A worked example

Divide 157 by 12.

What you enter

Dividend: 157
Divisor: 12

Step by step

Step 1: 15 ÷ 12 = 1; 1 × 12 = 12; 15 − 12 = 3; bring down the 7 to make 37
Step 2: 37 ÷ 12 = 3; 3 × 12 = 36; 37 − 36 = 1
Check: 13 × 12 + 1 = 157
As a decimal: 13.083333…, the 3 repeating forever

13 R 1, which is 13 1/12 or 13.083333…

12 does not go into 1, so the first step uses the first two digits, 15. That is why the answer has two digits, not three.

Long division questions, worked out

Each one divided digit by digit, exactly as the calculator above shows it.

1.What is 4,567 divided by 8?
1. 45 ÷ 8 = 5 (write 5 in the answer). 5 × 8 = 40. 45 − 40 = 5. Bring down the 6 to make 56.
2. 56 ÷ 8 = 7 (write 7 in the answer). 7 × 8 = 56. 56 − 56 = 0. Bring down the 7 to make 7.
3. 7 ÷ 8 = 0 (write 0 in the answer). 0 × 8 = 0. 7 − 0 = 7.
4. That uses every digit: 4,567 ÷ 8 = 570 remainder 7. For the decimal, write a decimal point in the answer and bring down a 0 to make 70. 70 ÷ 8 = 8 (write 8 in the answer). 8 × 8 = 64. 70 − 64 = 6. Bring down the 0 to make 60.
570 R 7, or 570.875 as a decimal.
2.What is 100 ÷ 3 with a remainder?
1. 10 ÷ 3 = 3 (write 3 in the answer). 3 × 3 = 9. 10 − 9 = 1. Bring down the 0 to make 10.
2. 10 ÷ 3 = 3 (write 3 in the answer). 3 × 3 = 9. 10 − 9 = 1.
33 R 1. As a decimal, 33.333333…, with the 3 repeating forever.
3.What is 1 ÷ 7 as a decimal?
1. That uses every digit: 1 ÷ 7 = 0 remainder 1. For the decimal, write a decimal point in the answer and bring down a 0 to make 10. 10 ÷ 7 = 1 (write 1 in the answer). 1 × 7 = 7. 10 − 7 = 3. Bring down the 0 to make 30.
2. 30 ÷ 7 = 4 (write 4 in the answer). 4 × 7 = 28. 30 − 28 = 2. Bring down the 0 to make 20.
3. 20 ÷ 7 = 2 (write 2 in the answer). 2 × 7 = 14. 20 − 14 = 6. Bring down the 0 to make 60.
0.142857… The six digits 142857 repeat forever.
4.Divide 8.36 by 4.
1. 8 ÷ 4 = 2 (write 2 in the answer). 2 × 4 = 8. 8 − 8 = 0.
2. Write the decimal point in the answer, above the one in the dividend, and bring down the 3 to make 3. 3 ÷ 4 = 0 (write 0 in the answer). 0 × 4 = 0. 3 − 0 = 3. Bring down the 6 to make 36.
3. 36 ÷ 4 = 9 (write 9 in the answer). 9 × 4 = 36. 36 − 36 = 0.
2.09.
5.What is 7 divided by 0.25?
1. The divisor 0.25 has 2 decimal places, so move the decimal point 2 places right in both numbers: 7 ÷ 0.25 becomes 700 ÷ 25. The answer is the same.
2. 70 ÷ 25 = 2 (write 2 in the answer). 2 × 25 = 50. 70 − 50 = 20. Bring down the 0 to make 200.
3. 200 ÷ 25 = 8 (write 8 in the answer). 8 × 25 = 200. 200 − 200 = 0.
28. Dividing by a quarter is the same as multiplying by 4.

Assumptions

Every result here rests on these. Change your inputs and the result changes with them.

The dividend and divisor are positive. For negative numbers, divide the sizes and make the answer negative if exactly one of them was negative.
The remainder is given only when both numbers are whole. With decimals, the answer is the decimal.

What this cannot tell you

Up to 15 digits in each number.
The calculator looks up to 60 decimal places for the repeat. A decimal whose repeating block is longer than that (1 ÷ 97 repeats every 96 digits) is shown to 20 places and marked.
The steps are written as a numbered list rather than drawn in the bracket layout used on paper; the steps are the same.

Questions people ask

How do you do long division step by step?

Divide, multiply, subtract, bring down, and repeat. For 157 ÷ 12: 12 goes into 15 once, 1 × 12 = 12, 15 − 12 = 3. Bring down the 7 to make 37. 12 goes into 37 three times, 3 × 12 = 36, 37 − 36 = 1. No digits are left, so the answer is 13 remainder 1.

How do you write a remainder as a fraction or a decimal?

Put the remainder over the divisor: 13 R 1 from dividing by 12 is 13 1/12. For the decimal, keep dividing past the decimal point, bringing down zeros: 157 ÷ 12 = 13.0833…, with the 3 repeating.

How do you divide by a decimal?

Move the decimal point in the divisor to the right until it is a whole number, and move it the same number of places in the dividend. 7 ÷ 0.25 becomes 700 ÷ 25, which is 28. Multiplying both numbers by the same amount does not change the answer.

Why does the decimal repeat?

Past the last digit of the dividend, every step brings down a 0, so each step depends only on the remainder. There are only so many possible remainders, fewer than the divisor, so one must eventually come back, and from then on the same digits repeat. If the remainder reaches 0 instead, the decimal ends.

Sources and review

Sources

Methodology version 1.0.0 · Last reviewed October 12, 2026

Cite this calculator

For coursework, a resource list or your own site. How every calculator is built and checked is set out on the methodology page.

Citation

Chalk Calculator. (2026, October 12). Long Division Calculator (Methodology version 1.0.0). https://chalkcalculator.com/long-division-calculator/

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