Long Division Calculator
Long division laid out the school way with every divide, multiply, subtract and bring-down step, plus the remainder and any repeating decimal.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Long Division Calculator?
Type a dividend and a divisor and the calculator sets out the long division the way it is written on paper: the divisor outside the bracket, the quotient on top, and each product and remainder stacked below with the next digit brought down. Every step is also written in words underneath.
You get the answer three ways: quotient with remainder (7452 ÷ 13 = 573 R 3), as an exact fraction or mixed number, and as a decimal. When the decimal repeats, the repeating block is found exactly and shown in parentheses, for example 1 ÷ 7 = 0.(142857). Choose how many decimal places to carry on into in the layout when you want to practise dividing past the point.
Decimal divisors are handled the way teachers show it: both numbers are multiplied by the same power of ten so the divisor becomes whole, and the page explains that shift.
- School-style layout with the quotient above the bracket
- Every step written in words as well
- Quotient and remainder, mixed number and decimal answers
- Exact repeating-decimal detection
- Decimal divisors scaled and explained
How to use the Long Division Calculator
- Type the dividend (the number being divided) and the divisor (what you divide by).
- Optionally choose how many decimal places to work in the layout. Leave it at "stop at the remainder" for whole-number answers.
- Read the quotient and remainder, the exact decimal, and the fraction in the result cards.
- Follow the layout from top to bottom: each "−" line is a product, and the line below it is the remainder with the next digit brought down.
- Read "Each step in words" for the same working in sentences, then copy or share.
Worked examples
With a remainder
Input
7452 ÷ 13
Output
573 R 3 = 573 3/13 = 573.(230769)
13 into 74 is 5 (65, remainder 9); into 95 is 7 (91, remainder 4); into 42 is 3 (39, remainder 3). Check: 573 × 13 + 3 = 7452.
A zero inside the quotient
Input
1035 ÷ 5
Output
207
After 10 ÷ 5 = 2, the next number is 3, which 5 goes into 0 times. Forgetting that 0 is the most common long-division mistake.
A repeating decimal
Input
1 ÷ 7, worked to 6 places
Output
0.(142857)
The remainders run 3, 2, 6, 4, 5, 1 and then repeat, so the six digits 142857 repeat forever.
A decimal divisor
Input
7.5 ÷ 0.25
Output
30
Multiplying both by 100 gives 750 ÷ 25, which is the same division with a whole-number divisor.
Background and insight
Long division repeats one cycle: divide, multiply, subtract, bring down. At each step you ask how many times the divisor fits into the current number, write that digit in the quotient, subtract the product, and bring down the next digit. Each digit is the largest that keeps the remainder smaller than the divisor, which is why the method always works.
A remainder can be written three ways. 7452 ÷ 13 is 573 R 3, the mixed number 573 3/13, or the decimal 573.230769230769… The check is that quotient × divisor + remainder gives back the dividend: 573 × 13 + 3 = 7452.
Carrying on past the decimal point, each step's remainder is less than the divisor, so there are only so many possible remainders. As soon as one repeats, the digits repeat too. That proves every fraction has a decimal that either ends or repeats, and that the repeating block for n/d is at most d − 1 digits long. 1/7 uses the maximum six digits; 1/97 repeats every 96. The calculator finds the cycle by remembering each remainder.
Common use cases
Learning the method
See exactly where each digit of the quotient comes from and check each line of a worksheet.
Helping with homework
Parents can follow the same layout their child is taught and spot the step that went wrong.
Fractions to decimals
Turn a fraction into its exact repeating decimal and find the length of the repeating block.
Sharing and packing
Find how many full boxes of 13 come from 7,452 items and how many are left over.
Tips and limitations
- If a step's remainder is not smaller than the divisor, the quotient digit was too small. If the product is bigger than the number above it, the digit was too large.
- When the divisor does not fit, write 0 in the quotient and bring down the next digit; do not skip the column.
- For a decimal divisor, move both decimal points the same number of places to the right first.
- To round, work one more decimal place than you need and look at that digit.
- Very large numbers are allowed (up to 40 digits), but the layout shows the first 45 steps.
Frequently asked questions
What are the steps of long division?
Divide, multiply, subtract, bring down, and repeat. Find how many times the divisor fits into the current number, write that digit on top, multiply it by the divisor, subtract, then bring down the next digit of the dividend.
How do you write a remainder as a decimal or fraction?
Put the remainder over the divisor to get the fraction part: 573 R 3 for ÷ 13 is 573 3/13. For the decimal, keep dividing past the decimal point by adding zeros, or divide the remainder by the divisor: 3 ÷ 13 = 0.230769…
How do I divide by a decimal?
Multiply the divisor and the dividend by the same power of 10 so the divisor becomes a whole number. 7.5 ÷ 0.25 becomes 750 ÷ 25 = 30. The answer does not change because both numbers were scaled equally.
How do I know if a decimal will repeat?
Simplify the fraction first. If the denominator has only 2s and 5s as prime factors the decimal ends; otherwise it repeats. 3/8 = 0.375 ends, while 5/12 = 0.41(6) repeats.
What does 0.(142857) mean?
The digits in parentheses repeat forever, so 0.(142857) is 0.142857142857… Some books put a bar over the repeating digits instead. Both mean exactly 1/7.
How do I check a long division answer?
Multiply the quotient by the divisor and add the remainder. If you get the dividend back, the division is right. For 7452 ÷ 13: 573 × 13 = 7449, plus 3 is 7452.
Is there an in-depth guide to the Long Division Calculator?
Yes. “Percentages, Fractions and Ratios: How the Arithmetic Fits Together” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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