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CalcChef

Long Division Calculator

Long division of two numbers with every step shown: quotient, remainder, exact fraction, the decimal with its repeating digits marked, and the working. How it works

Use the Long Division Calculator

Numbers of up to 100 digits, with an optional sign and decimal point (12.5 ÷ 2 is worked as 125 ÷ 20). Decimal places: 0 to 100. Negative numbers: the digits are divided as positive numbers, the quotient is cut off toward zero, and the remainder has the sign of the dividend, so dividend = divisor × quotient + remainder.

Quotient
493
Remainder 20

12345 ÷ 25 = 493 remainder 20 = 493.8

Decimal to 10 places
493.8
Exact fraction
2469/5
Mixed number
493 4/5
Exact decimal
493.8

The decimal ends. Digits are cut off at the chosen number of places, not rounded.

Long division layout

       493.8
   ┌────────
25 │ 12345.0
    −100
    ────
      234
     −225
     ────
        95
       −75
       ───
         200
        −200
        ────
           0

The steps in words

  1. Step 1: Start with 123, the first digits of the dividend that make a number of at least 25. 25 goes into 123 4 times: write 4 in the quotient, subtract 4 × 25 = 100, remainder 23.
  2. Step 2: Bring down 4 to make 234. 25 goes into 234 9 times: write 9 in the quotient, subtract 9 × 25 = 225, remainder 9.
  3. Step 3: Bring down 5 to make 95. 25 goes into 95 3 times: write 3 in the quotient, subtract 3 × 25 = 75, remainder 20.
  4. Step 4: Bring down a 0 after the decimal point to make 200. 25 goes into 200 8 times: write 8 in the quotient, subtract 8 × 25 = 200, remainder 0.

About the Long Division Calculator

12345 ÷ 25 = 493 remainder 20, or 493.8 as a decimal and 2469/5 (493 4/5) as a fraction. This long division calculator works a division the way it is done on paper and shows every step: each subtraction, each digit brought down, the quotient, the remainder, the exact fraction and mixed number, and the decimal, with repeating digits marked.

1 ÷ n as a decimal, for n = 2 to 13

DivisionExact decimalTo 10 placesRepeating block
1 ÷ 20.50.5None, the decimal ends
1 ÷ 30.(3)0.3333333333…1 digit
1 ÷ 40.250.25None, the decimal ends
1 ÷ 50.20.2None, the decimal ends
1 ÷ 60.1(6)0.1666666666…1 digit
1 ÷ 70.(142857)0.1428571428…6 digits
1 ÷ 80.1250.125None, the decimal ends
1 ÷ 90.(1)0.1111111111…1 digit
1 ÷ 100.10.1None, the decimal ends
1 ÷ 110.(09)0.0909090909…2 digits
1 ÷ 120.08(3)0.0833333333…1 digit
1 ÷ 130.(076923)0.0769230769…6 digits

Digits in brackets repeat forever. The 10-place figure is cut off, not rounded, which is why 1 ÷ 6 ends in 6 and not 7.

Worked divisions: quotient, remainder and decimal

DivisionQuotientRemainderExact decimal
12345 ÷ 2549320493.8
100 ÷ 714214.(285714)
22 ÷ 7313.(142857)
365 ÷ 752152.(142857)
1000 ÷ 33331333.(3)
1000 ÷ 1662862.5
125 ÷ 815515.625
144 ÷ 1212012
5280 ÷ 124400440
86400 ÷ 712342612342.(857142)
12.5 ÷ 260.56.25
-7 ÷ 2-3-1-3.5
7 ÷ -2-31-3.5

Check any row with dividend = divisor × quotient + remainder: 25 × 493 + 20 = 12345.

How to use this tool

  1. Type the dividend (the number being divided) and the divisor (the number you divide by). Each can have up to 100 digits, a decimal point and a minus sign.
  2. Set how many decimal places to continue to, from 0 to 100. The field starts at 10.
  3. Read the quotient and remainder, then follow the layout and the list of steps in words.

Frequently asked questions

How do you do long division step by step?
Divide, multiply, subtract, bring down, and repeat. For 100 ÷ 7: 7 goes into 10 once, leaving 3. Bring down 0 to make 30, and 7 goes into 30 four times (28), leaving 2. The answer is 14 remainder 2.
How do I turn a remainder into a decimal?
Put a decimal point after the quotient, bring down a 0 beside the remainder and keep dividing. 17 ÷ 5 is 3 remainder 2. Bring down a 0 to make 20, and 5 goes into 20 four times, so 17 ÷ 5 = 3.4. As a fraction the remainder goes over the divisor: 17 ÷ 5 = 3 2/5, or 17/5, and the tool shows both forms.
What is 1 divided by 3 as a decimal?
0.(3): the 3 repeats forever, because the remainder is 1 at every step. Set to 4 decimal places, the tool shows 0.3333… for 1 ÷ 3 and 0.6666… for 2 ÷ 3, cut off and not rounded up to 0.6667.
How do I divide decimals with long division?
Move the decimal point the same number of places in both numbers until both are whole. 3.6 ÷ 0.12 becomes 360 ÷ 12 = 30, and 12.5 ÷ 2 becomes 125 ÷ 20 = 6.25. The tool does this scaling and says so under the result.
How does it divide negative numbers?
It divides the digits as positive numbers and then sets the signs. The quotient is truncated toward zero (the fraction is dropped) and the remainder has the sign of the dividend: -7 ÷ 2 = -3 remainder -1, and 7 ÷ -2 = -3 remainder 1. Floored division, which some textbooks and programming languages use, gives -4 remainder 1 for -7 ÷ 2.
Why do some decimals repeat?
Every step leaves a remainder smaller than the divisor, so only so many remainders are possible. When one comes back, the same digits follow again. That is why the repeating block of 1 ÷ 7 has 6 digits, one fewer than the divisor, and could not have more.

Quotient, remainder and repeating decimal in one run

Checking homework line by line against the layout, which shows each subtraction and each digit brought down as on paper. Finding a quotient and remainder: 365 ÷ 7 = 52 remainder 1, so 365 days are 52 full weeks and 1 day. Reading the exact decimal with the repeating part marked, 22 ÷ 7 = 3.(142857), and the exact fraction: 22/7, or the mixed number 3 1/7.

Divide, multiply, subtract, bring down

Long division works through the dividend from the left, one digit at a time.

  1. See how many times the divisor goes into the current number and write that digit in the quotient.

  2. Multiply the digit by the divisor and subtract.

  3. Bring down the next digit of the dividend beside what is left.

When the digits run out, what is left is the remainder:

dividend = divisor × quotient + remainder

Worked example, 12345 ÷ 25: 25 goes into 123 four times (100), leaving 23. Bring down 4 to make 234: nine times (225), leaving 9. Bring down 5 to make 95: three times (75), leaving 20. So 12345 ÷ 25 = 493 remainder 20. Bringing down a 0 after the decimal point makes 200, which is 8 × 25, so the decimal answer is 493.8.

The decimal goes on to the number of places you choose, from 0 to 100, next to the exact decimal. When a remainder comes back a second time, the digits since its first appearance repeat forever and are put in brackets: 1 ÷ 6 = 0.1(6). Each number can have up to 100 digits. Decimals are scaled to whole numbers first, so 12.5 ÷ 2 is worked as 125 ÷ 20, but the remainder is given in the units you typed: 12.5 ÷ 2 = 6 remainder 0.5, since 2 × 6 + 0.5 = 12.5.

Fun Fact: 1 ÷ 81 = 0.(012345679): the repeating block runs through the digits in order and skips only the 8.

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