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Long Division Calculator

Work through long division one step at a time, and get an answer with a remainder or a decimal with any repeating digits marked.

Level: Grades 5–7

  • Common Core standard 6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.
  • Common Core standard 5.NBT.B.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • Common Core standard 7.NS.A.2.dConvert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Printable worksheet

Long Division Calculator

Inputs
Answer as

A whole number other than 0, up to 10^12 in size.

Result

Answer

360 R 5

4,325 ÷ 12 = 360 R 5.

Quotient
360
Remainder
5
As a mixed number
360 5/12

See the step-by-step solution ↓

Step-by-step solution

  1. Start with 43, the first part of 4,325 that is at least 12. 12 goes into it 3 times; multiply and subtract

    43−3×12=7

  2. Bring down the next digit, 2, to make 72. 12 goes into it 6 times; multiply and subtract

    72−6×12=0

  3. Bring down the next digit, 5, to make 5. 12 goes into it 0 times; multiply and subtract

    5−0×12=5

  4. No digits are left to bring down, so the quotient is 360 and the last subtraction leaves the remainder

    4,325 ÷ 12 = 360 R 5

  5. Check: quotient × divisor + remainder gives back the dividend

    360 × 12 + 5=4,325

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Divide one whole number by another and see every step of long division written out, just as you'd do it on paper. Long division handles a big division one digit at a time. At each stage you ask how many times the divisor (the number you're dividing by) fits into the part you're working on. You write that digit in the answer, multiply, subtract, and bring down the next digit. It turns one hard division into a string of small ones. It's still the clearest way to see where a remainder or a repeating decimal comes from.

Enter a dividend (the number being divided) and a divisor. Then choose your answer as a quotient and remainder, such as 360 R 5, or as a decimal. The quotient is the whole-number answer. In decimal mode, the calculator keeps bringing down zeros. When a remainder comes back that it has seen before, the digits must repeat from there. So it puts the repeating block in brackets: 1 ÷ 7 = 0.(142857). Every row of the division appears in the working, laid out as the multiply-and-subtract you'd write by hand.

Where it's used

Why this math matters outside the classroom:

  • Splitting a bill. Five coworkers splitting a $1,260 bill each pay 1,260 ÷ 5 = $252.
  • Packing boxes. A warehouse packing 1,000 items 24 to a box fills 41 boxes with 16 items left over.
  • Fuel economy. A driver who used 12 gallons over 354 miles gets 354 ÷ 12 = 29.5 miles per gallon.
  • Repeating decimals. Dividing 1 by 7 by hand shows the block 142857 repeating forever, because the remainders start to cycle.
  • Unit prices. A shopper divides $4.68 by 12 to find that each can in a 12-pack costs $0.39.

Grade level and standards: Grades 5–7; Common Core State Standards for Mathematics 6.NS.B.2, 5.NBT.B.6, 7.NS.A.2.d. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose the answer type: quotient and remainder, or decimal.
  2. Enter the dividend (the number being divided) and the divisor (the number you're dividing by).
  3. In decimal mode, choose how many decimal places to round to.
  4. Read the answer at the top. Then open the working to follow each bring-down, multiply and subtract.

What the inputs mean

Dividend (number being divided)
A whole number, positive or negative, up to about 9 quadrillion in size. To divide decimals, first multiply both numbers by the same power of 10, such as 10 or 100. For example, 4.5 ÷ 0.3 is the same as 45 ÷ 3.
Divisor (number to divide by)
A whole number other than 0, up to one trillion (10^12) in size.
Decimal places
Used for the rounded answer (rounding half up). The exact repeating form is found separately, and this setting doesn't change it.

Formula and method

dividend = quotient × divisor + remainder,   0 ≤ remainder < divisor
each row: (remainder × 10 + next digit) − q × divisor = new remainder
the decimal repeats as soon as a remainder repeats

In the formulas, the dividend is the number being divided and the divisor is the number you divide by. The quotient is the whole-number answer, and the remainder is what's left over. The letter q is the digit you write in the answer on each row. On each row, you find the largest digit q where q × divisor still fits, and subtract. The new remainder is always smaller than the divisor. Bringing down the next digit multiplies it by 10 and adds that digit. When the dividend's digits run out, the digits written so far are the quotient. The last subtraction leaves the remainder.

To keep going past the decimal point, bring down zeros. Every remainder is a whole number from 0 up to one less than the divisor. So within that many steps, one of two things happens. Either a remainder of 0 appears and the decimal ends, or some remainder shows up again. The same remainder always leads to the same digits. So the digits between its two appearances repeat forever. That block is shown in brackets. Many textbooks draw a bar over it instead.

Here's a handy rule. Write the division as a fraction and reduce it as far as it goes (lowest terms). The decimal ends only if the bottom number breaks down into 2s and 5s alone, with no other prime factors. So 3/8 ends (0.375), while 1/6 = 0.1(6) and 1/7 = 0.(142857) repeat.

Worked example

Divide 4,325 by 12.

  1. 12 doesn't go into 4, so start with 43. 12 goes into 43 three times: 43 − 3 × 12 = 7.
  2. Bring down the 2 to make 72. 12 goes into 72 six times: 72 − 6 × 12 = 0.
  3. Bring down the 5 to make 5. 12 goes into 5 zero times: 5 − 0 × 12 = 5. No digits are left, so 4,325 ÷ 12 = 360 R 5.
  4. In decimal mode, bring down a 0 to make 50: 50 − 4 × 12 = 2. Then 20 − 1 × 12 = 8, then 80 − 6 × 12 = 8.
  5. The remainder 8 has already appeared, so the digit 6 repeats forever.

Result: 4,325 ÷ 12 = 360 R 5, or 360 5/12 as a mixed number. As a decimal it's 360.41(6), which rounds to 360.4166666667 at 10 decimal places.

Understanding the result

The remainder is what's left after sharing out as many whole groups as you can. Sharing 4,325 items among 12 people gives each person 360, with 5 left over.

A block in brackets repeats without end. 360.41(6) means 360.416666…. The length of the block, called its period, can be as long as the divisor minus 1. For example, 1/97 has a block 96 digits long.

For negative numbers, the calculator divides the numbers without their signs, then adds the sign back. In remainder mode, the remainder takes the sign of the dividend, the rule most programming languages use. For the other rules, use the modulo calculator.

Assumptions and limitations

  • Both numbers are whole numbers, and the divisor isn't 0.
  • Rounding to your chosen places is half up (away from zero).
  • The working shows at most 40 decimal rows. Longer answers are summarized.
  • Repeating blocks are searched for up to 10,000 decimal digits. Only blocks of up to 120 digits are printed in full.
  • Decimal dividends and divisors must be turned into whole numbers first.

Frequently asked questions

What does the R in 360 R 5 mean?

R stands for remainder. 12 fits into 4,325 a whole 360 times, with 5 left over. You can also write the same answer as the mixed number 360 5/12.

How do I know if a decimal will repeat?

Reduce the fraction to lowest terms and break the bottom number into prime factors. If it has any prime factor other than 2 or 5, the decimal repeats. Otherwise, it ends. For example, 7/20 = 0.35 ends because 20 = 2² × 5.

Why does long division of whole numbers always end or repeat?

Each remainder is less than the divisor, so there are only so many remainders possible. Once a remainder reaches 0, the division stops. If it never does, some remainder must come back eventually. From then on, the digits go round in a cycle.

What's the difference between long and short division?

They're the same method. Short division keeps the remainders in your head, or as small carried digits. That works well when you divide by a single digit. Long division writes out each multiply-and-subtract, which is easier to check with bigger divisors.

How this calculator is checked

Method: Standard long-division algorithm; repetend detection by tracking remainders (pigeonhole principle). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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