Long Division Calculator That Shows and Explains Each Step

Long Division Calculator Sign

This calculator will divide one number (dividend) by another number (divisor) using the long division method, and show and explain each step.

The calculator will accommodate divisors and dividends containing decimal points and will give the remainder in both the whole number and the decimal format.

Plus, unlike other online long division calculators, the calculated results will list the 1-9 multiples of the divisor to help you learn your factors, and will also report the detection of patterns which may indicate the result is a recurring decimal.

Note that you are looking to multiply decimals, integers, or whole numbers, check out the Long Multiplication Calculator.

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Long Division Calculator

Divide one number by another and see how the result is arrived at using long division.

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Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Divisor:Divisor:Divisor:Divisor:

Divisor:

Enter the divisor in the left-hand field on the line below (number greater than zero). The divisor is the number being divided into another number. If the divisor you enter is greater than the dividend, the result will be a decimal number less than 1.

Dividend:Dividend:Dividend:Dividend:

Dividend:

Enter the dividend in the right-hand field on the line below (number greater than zero). The dividend is the number being divided by another number.

#
#
Quotient:Division quotient:Long division quotient:Long division quotient:

Long division quotient:

This is the result the long division calculator stopped at. Please double check this result with the result on the next line.

Calculated:Calculated quotient:Calculated division quotient:Calculated division quotient:

Calculated division quotient:

This is the result you would likely get if you used a standard calculator for the division. This result is provided as a means to check the long division result for accuracy. Note that if the result contains more than 16 digits the last digit(s) is likely rounded.

Whole num:Whole number:Whole number portion of quotient:Whole number portion of quotient:

Whole number portion of quotient:

This is the whole number portion of the quotient. The quotient is the result of dividing one number by another.

Remainder:Remainder:Remainder:Remainder:

Remainder:

This is what is left after multiplying the whole number portion of the quotient by the divisor, and then subtracting that result from the dividend.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

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Help and Tools

Learn

How to do long division.

To show you how to do long division I will give the actual calculator results involving four common long division scenarios:

  • Dividing whole numbers with no remainder.
  • Dividing whole numbers with whole remainder.
  • Dividing decimal numbers with no remainder.
  • Dividing decimal numbers with decimal remainder.

To follow the steps I took as I proceeded through each long division example, tap the info (i) icon on each row of the division process.

Dividing Whole Numbers With No Remainder

 « Quotient
Divisor »31443« Dividend
Multiples
of 3
13
26
39
412
515
618
721
824
927
  1234
  0481
 31443

Since 3 is greater than 1 you enter a zero in the 1st answer position and then combine the digit 1 with the digit from the next position in the dividend (4 in column #2) in order to form a number that is greater than or equal to the 3. That new number is 14.

Since the greatest multiple of 3 that divides into 14 without going over is 4 (4 x 3 = 12), you enter 4 in the 2nd answer position and 12 in the subtraction row.

Since 14 minus 12 leaves a remainder of 2 you enter 2 on the next line. Then move the next dividend digit (4 in column #3) down to that line to form the new subtrahend of 24.

-12  

Since the greatest multiple of 3 that divides into 24 without going over is 8 (8 x 3 = 24), you enter 8 in the 3rd answer position and 24 in the subtraction row.

Since 24 minus 24 leaves a remainder of 0 you enter 0 on the next line. Then move the next dividend digit (3 in column #4) down to that line to form the new subtrahend of 03.

  24 
- 24 

Since the greatest multiple of 3 that divides into 3 without going over is 1 (1 x 3 = 3), you enter 1 in the 4th answer position and 3 in the subtraction row.

Since 3 minus 3 leaves a remainder of 0 you enter 0 on the next line.

   03
-   3

Since all dividend digits have been moved down, and the remainder is zero, the problem is solved.

    0
-    

Since 3 x 481 does equal 1443, our solution checks out.

Dividing Whole Numbers With Remainder

 « Quotient
Divisor »5123« Dividend
Multiples
of 5
15
210
315
420
525
630
735
840
945
  123
  024
 5123

Since 5 is greater than 1 you enter a zero in the 1st answer position and then combine the digit 1 with the digit from the next position in the dividend (2 in column #2) in order to form a number that is greater than or equal to the 5. That new number is 12.

Since the greatest multiple of 5 that divides into 12 without going over is 2 (2 x 5 = 10), you enter 2 in the 2nd answer position and 10 in the subtraction row.

Since 12 minus 10 leaves a remainder of 2 you enter 2 on the next line. Then move the next dividend digit (3 in column #3) down to that line to form the new subtrahend of 23.

-10 

Since the greatest multiple of 5 that divides into 23 without going over is 4 (4 x 5 = 20), you enter 4 in the 3rd answer position and 20 in the subtraction row.

Since 23 minus 20 leaves a remainder of 3 you enter 3 on the next line.

  23
- 20

Since all dividend digits have been moved down and you are left with the number 3, the remainder is 3.

   3

Since 5 x 24 + 3 does equal 123, our solution checks out.

Dividing Decimal Numbers With No Remainder

 « Quotient
Divisor »5.5220« Dividend
Multiples
of 55
155
2110
3165
4220
5275
6330
7385
8440
9495
   1234
   0040

The first step in solving the problem is to get rid of the decimal point in the divisor 5.5.

To do that, you move the decimal point 1 place to the right in both the divisor 5.5 and the dividend 220.

Moving the decimal point 1 place to the right in the divisor changes it to 55.

Since the dividend (220) has no decimal places, you simply add a zero for each decimal place you moved in the divisor. This leaves you with a new dividend of 2200.

Note that a vertical red line indicates the position of the decimal point within the quotient (if applicable).

552200

Since 55 is greater than 2 you enter a zero in the 1st quotient position and then combine the digit 2 with the digit from the next position in the dividend (2 in column #2) in an attempt to form a number that is greater than or equal to the 55. That new number is 22.

Since 55 is greater than 22 you enter a zero in the 2nd quotient position and then combine the digits 22 with the digit from the next position in the dividend (0 in column #3) in an attempt to form a number that is greater than or equal to the 55. That new number is 220.

Since the greatest multiple of 55 that divides into 220 without going over is 4 (4 x 55 = 220), you enter 4 in the 3rd quotient position and 220 in the subtraction row.

Since 220 minus 220 leaves a remainder of 0 you enter 0 on the next line. Then move the next dividend digit (0 in column #4) down to that line to form the new subtrahend of 00.

-220 

The problem appears to be solved.

    0
-    

Since 5.5 x 40 does equal 220, our solution checks out.

Dividing Decimal Numbers With Decimal Remainder

 « Quotient
Divisor »3.3399.99« Dividend
Multiples of 333
1333
2666
3999
41332
51665
61998
72331
82664
92997
    12345678910111213
    0030027027027

The first step in solving the problem is to get rid of the decimal point in the divisor 3.33.

To do that, you move the decimal point 2 places to the right in both the divisor 3.33 and the dividend 99.99.

Moving the decimal point 2 places to the right in the divisor changes it to 333.

Since the dividend (99.99) already has 2 decimal places, you simply move the decimal point 2 places to the right. This leaves you with a new dividend of 9999.

Next, continue to add zeros to the dividend as needed until you either solve the division, or you reach the desired number of decimal places.

Note that a vertical red line indicates the position of the decimal point within the quotient (if applicable).

3339999000000000

Since 333 is greater than 9 you enter a zero in the 1st quotient position and then combine the digit 9 with the digit from the next position in the dividend (9 in column #2) in an attempt to form a number that is greater than or equal to the 333. That new number is 99.

Since 333 is greater than 99 you enter a zero in the 2nd quotient position and then combine the digits 99 with the digit from the next position in the dividend (9 in column #3) in an attempt to form a number that is greater than or equal to the 333. That new number is 999.

Since the greatest multiple of 333 that divides into 999 without going over is 3 (3 x 333 = 999), you enter 3 in the 3rd quotient position and 999 in the subtraction row.

Since 999 minus 999 leaves a remainder of 0 you enter 0 on the next line. Then move the next dividend digit (9 in column #4) down to that line to form the new subtrahend of 09.

-999          

Since 333 is greater than 9 you enter a zero in the 4th quotient position and then combine the digits 9 with the digit from the next position in the dividend (0 in column #5) in an attempt to form a number that is greater than or equal to the 333. That new number is 90.

Since 333 is greater than 90 you enter a zero in the 5th quotient position and then combine the digits 90 with the digit from the next position in the dividend (0 in column #6) in an attempt to form a number that is greater than or equal to the 333. That new number is 900.

Since the greatest multiple of 333 that divides into 900 without going over is 2 (2 x 333 = 666), you enter 2 in the 6th quotient position and 666 in the subtraction row.

Since 900 minus 666 leaves a remainder of 234 you enter 234 on the next line. Then move the next dividend digit (0 in column #7) down to that line to form the new subtrahend of 2340.

   0900       
-   666       

Since the greatest multiple of 333 that divides into 2340 without going over is 7 (7 x 333 = 2331), you enter 7 in the 7th quotient position and 2331 in the subtraction row.

Since 2340 minus 2331 leaves a remainder of 9 you enter 9 on the next line. Then move the next dividend digit (0 in column #8) down to that line to form the new subtrahend of 90.

    2340      
-   2331      

Since 333 is greater than 90 you enter a zero in the 8th quotient position and then combine the digits 90 with the digit from the next position in the dividend (0 in column #9) in an attempt to form a number that is greater than or equal to the 333. That new number is 900.

Since the greatest multiple of 333 that divides into 900 without going over is 2 (2 x 333 = 666), you enter 2 in the 9th quotient position and 666 in the subtraction row.

Since 900 minus 666 leaves a remainder of 234 you enter 234 on the next line. Then move the next dividend digit (0 in column #10) down to that line to form the new subtrahend of 2340.

       900    
-      666    

Since the greatest multiple of 333 that divides into 2340 without going over is 7 (7 x 333 = 2331), you enter 7 in the 10th quotient position and 2331 in the subtraction row.

Since 2340 minus 2331 leaves a remainder of 9 you enter 9 on the next line. Then move the next dividend digit (0 in column #11) down to that line to form the new subtrahend of 90.

       2340   
-      2331   

Since 333 is greater than 90 you enter a zero in the 11th quotient position and then combine the digits 90 with the digit from the next position in the dividend (0 in column #12) in an attempt to form a number that is greater than or equal to the 333. That new number is 900.

Since the greatest multiple of 333 that divides into 900 without going over is 2 (2 x 333 = 666), you enter 2 in the 12th quotient position and 666 in the subtraction row.

Since 900 minus 666 leaves a remainder of 234 you enter 234 on the next line. Then move the next dividend digit (0 in column #13) down to that line to form the new subtrahend of 2340.

          900 
-         666 

Since the greatest multiple of 333 that divides into 2340 without going over is 7 (7 x 333 = 2331), you enter 7 in the 13th quotient position and 2331 in the subtraction row.

Since 2340 minus 2331 leaves a remainder of 9 you enter 9 on the next line.

          2340
-         2331

It appears the calculator ran out of room before it could complete the long division.

             9
-             

Since 3.33 x 30.027027027 does not equal 99.99, either the calculator ran out of room before the long division was completed, the quotient contains a recurring decimal, or there is a rounding issue between the calculated result and the long division result. In this case it appears to be a repeating decimal.

I hope I"ve managed to help you to understand how to perform long division. If not, please use the feedback form beneath the calculator to let me know what I have left out.

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.