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Welcome to the our Step by Step Long Division page.

Find out how long division works and solve your own long division problems step-by-step the easy way with our calculator.

Take a look at some of our worked examples or try some of our practice worksheets.

### Parts of a Long Division Equation

The dividend is the number being divided.

The divisor is the number you are dividing by.

The quotient is the number of times the divisor goes into the dividend.

The remainder is what is left over from the dividend when the divisor has been taken away as many times as it can be without leading to a negative answer.

The remainder can be a whole number, but it can also be expressed as a fraction or decimal.

### The Steps in Long Division

#### When we are doing long division, we can split the method into a series of stages with each stage having 4 steps:

#### Here are the 4 steps in each stage.

- Divide
- Multiply
- Subtract
- Bring the next number(s) down

This calculator will help you to use long division to solve your own division problems.

Simply enter the dividend in the first box and the divisor in the 2nd box.

Click on the 'Get Answer' box to find the answer and get the step-by-step working out you need!

The calculator will show you the completed long division method first.

The calculator will then break up the long division method into stages and steps so that you can follow it through from beginning to end so see all the working out.

### Examples of Step by Step Long Division

Here are some examples showing some step by step long division problems with answers, along with commentary on each step.

#### Example 1) Work out 84 ÷ 3

So we are working out\[ 3 \enclose {longdiv} {84} \]

#### Stage 1

Step 1) Divide

First step is to work out 8 ÷ 3, which means we need to find how many groups of 3 make 8.

We can get 2 groups of 3 in 8 so we write a 2 on the answer line above the 8:\[ \begin {array}{l} \quad 2 \\3 \enclose {longdiv} {84} \\\end{array} \]

Step 2) Multiply

We multiply the number of groups by the divisor: 2 x 3 = 6 and write this underneath the 8:\[ \begin {array}{l} \quad 2 \\3 \enclose {longdiv} {84} \\\quad \underline{6}\end{array} \]

Step 3) Subtract

Next we subtract 6 from 8 to get 2 which we write underneath the 6.\[ \begin {array}{l} \quad 2 \\3 \enclose {longdiv} {84} \\\quad \underline{6} \\\quad 2\end{array} \]

Step 4) Bring down

The next step is to bring down the 4 and put it next to the 2\[ \begin {array}{l} \quad 2 \\3 \enclose {longdiv} {84} \\\quad \underline{6} \\\quad 24\end{array} \]

#### Stage 2

Step 1) Divide

We now have to work out 24 ÷ 3, or how many groups of 3 make 24.

There are 8 groups of 3 in 24. So we write an 8 on the answer line above the 4:\[ \begin {array}{l} \quad 28 \\3 \enclose {longdiv} {84} \\\quad \underline{6} \\\quad 24 \\\end{array} \]

Step 2) Multiply

8 groups of 3 make 24. We write this underneath the 24:\[ \begin {array}{l} \quad 28 \\3 \enclose {longdiv} {84} \\\quad \underline{6} \\\quad 24 \\\quad \underline{24}\end{array} \]

Step 3) Subtract

Finally subtract 24 from 24 to give us an answer of 0 which we write underneath the 24.\[ \begin {array}{l} \quad 28 \\3 \enclose {longdiv} {84} \\\quad \underline{6} \\\quad 24 \\\quad \underline{24} \\\quad \; \; 0\end{array} \]

Step 4) Bring down next digit

There are no more digits to bring down so we have finished. There is a 0 at the bottom of the long division which means there is no remainder.

Answer: 84 ÷ 3 = 28

The fact that there is no remainder means that the dividend, which is 84, is a multiple of the divisor, which is 3, and also that the divisor is a factor of the dividend!

For more information about Factors and Multiples, use the link below:

- Factors and Multiples Support

#### Example 2) Work out 347 ÷ 4

So we are working out\[ 4 \enclose {longdiv} {347} \]

#### Stage 1

Step 1) Divide

FIrst step is to work out 3 ÷ 4, which means we need to find how many groups of 4 make 3.

There are 0 groups of 4 in 3, so we write a 0 on the answer line above the 3 then keep the 3 in its place and go on to the next digit which is 4.

This gives us:\[ \begin {array}{l} \quad 0 \\4 \enclose {longdiv} {347}\end{array} \]

So we need to work out 34 ÷ 4, or find how many groups of 4 make 34.

We can get 8 groups of 4 in 34 so we write an 8 on the answer line above the 4.

This gives us:\[ \begin {array}{l} \quad 08 \\4 \enclose {longdiv} {347}\end{array} \]

Step 2) Multiply

8 groups of 4 make 32. We write this underneath the 34:\[ \begin {array}{l} \quad 08 \\4 \enclose {longdiv} {347} \\\quad \underline {32}\end{array} \]

Step 3) Subtract

We subtract 32 from 34 to give us an answer of 2 which we put underneath the 32:\[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 2 \end{array} \]

Step 4) Bring down next digit

Next we bring the 7 down alongside the 2.\[ \begin {array}{l} \quad 08 \\4 \enclose {longdiv} {347} \\\quad \underline {32} \\\quad \; \; 27\end{array} \]

#### Stage 2

Step 1) Divide

So we need to work out 27 ÷ 4, or find how many 4s make 27.

There are 6 groups of 4 in 27. So we write a 6 on the answer line above the 7:\[ \begin {array}{l} \quad 086 \\4 \enclose {longdiv} {347} \\ \quad \underline {32} \\\quad \; \; 27\end{array} \]

Step 2) Multiply

6 groups of 4 make 24. We write this underneath the 27:\[ \begin {array}{l} \quad 086 \\4 \enclose {longdiv} {347} \\ \quad \underline {32} \\\quad \; \; 27 \\ \quad \; \; \underline {24}\end{array} \]

Step 3) Subtract

Finally we need to subtract 24 from 27 to give us 3 which we put underneath the 24.

\[ \begin {array}{l} \quad 086 \\4 \enclose {longdiv} {347} \\\quad \underline {32} \\\quad \; \; 27 \\\quad \; \; \underline {24} \\\quad \quad 3\end{array} \]

Step 4) Bring down next digit

There are no more digits to bring down so we have finished. The 3 at the bottom of the long division is the remainder.

Answer: 347 ÷ 4 = 86r3

If we wanted the remainder as a fraction, we would have 347 ÷ 4 = 86 ¾

#### Example 3) Work out 8165 ÷ 12

So we are working out\[ 12 \enclose {longdiv} {8165} \]

#### Stage 1

Step 1) Divide

FIrst step is to work out 8 ÷ 12, which means we need to find how many groups of 12 make 8.

There are 0 groups of 12 in 8, so we keep the 8 in its place and put a zero above the 8 then go on to the next digit which is 1.

This gives us:\[ \begin {array}{l} \quad \; 0 \\12 \enclose {longdiv} {8165}\end{array} \]

So the next step is to work out 81 ÷ 12, or find how many groups of 12 make 81.

There are 6 groups of 12 in 81, so we put a 6 above the 1.

This gives us:\[ \begin {array}{l} \quad \; 06 \\12 \enclose {longdiv} {8165}\end{array} \]

Step 2) Multiply

6 groups of 12 make 72. We write this underneath the 81.\[ \begin {array}{l} \quad \; 06 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72}\end{array} \]

Step 3) Subtract

We subtract 72 from 81 to get 9 which goes underneath the 72:\[ \begin {array}{l} \quad \; 06 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72} \\\qquad 9\end{array} \]

Step 4) Bring down next digit

Next we bring the 6 down alongside the 9.\[ \begin {array}{l} \quad \; 06 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72} \\\qquad 96\end{array} \]

#### Stage 2

Step 1) Divide

So we need to work out 96 ÷ 12, or find how many 12s make 96.

There are 8 groups of 12 in 96, so we write 8 in the answer line above the 6.\[ \begin {array}{l} \quad \; 068 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72} \\\qquad 96\end{array} \]

Step 2) Multiply

8 groups of 12 make 96 which we write underneath:\[ \begin {array}{l} \quad \; 068 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72} \\\qquad 96 \\\qquad \underline{96}\end{array} \]

Step 3) Subtract

Now we subtract 96 from 96 to give us 0.\[ \begin {array}{l} \quad \; 068 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72} \\\qquad 96 \\\qquad \underline{96} \\\qquad \; \: 0\end{array} \]

Step 4) Bring down next digit

Now we bring down the 5.\[ \begin {array}{l} \quad \; 068 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72} \\\qquad 96 \\\qquad \underline{96} \\\qquad \; \: 05\end{array} \]

#### Stage 3

Step 1) Divide

Nexy we need to work out 5 ÷ 12, or how many 12s make 5.

There are 0 groups of 12 in 5, so we write 0 above the 5 digit in the answer line:\[ \begin {array}{l} \quad \; 0680 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72} \\\qquad 96 \\\qquad \underline{96} \\\qquad \; \: 05 \\\end{array} \]

Step 2) Multiply

0 groups of 12 make 0, so we write 0 under the 05:\[ \begin {array}{l} \quad \; 0680 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72} \\\qquad 96 \\\qquad \underline{96} \\\qquad \; \: 05 \\\qquad \; \: \underline {00}\end{array} \]

Step 3) Subtract

Subtracting 0 from 5 gives us 5.\[ \begin {array}{l} \quad \; 0680 \\12 \enclose {longdiv} {8165} \\\quad \; \, \underline {72} \\\qquad 96 \\\qquad \underline{96} \\\qquad \; \: 05 \\\qquad \; \: \underline {00} \\\qquad \quad 5\end{array} \]

Step 4) Bring down next digit

There are no more digits to bring down so we have finished. The 5 at the bottom of the long division is the remainder.

Answer: 8165 ÷ 12 = 680r5

If we wanted the remainder as a fraction, we would have\[ 8165 \div 12 = 680 {5 \over 12} \]

### More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

### Randomly Generated Long Division Problems Worksheet Generator

Take a look at our long division problems worksheet generator.

This generator will generate your own worksheets from 2-digits by 1-digit to 5-digits by 2-digits.

You can choose to have remainders or not, and whether to record the remainders as a whole number or fraction.

- Long Division Problems with Answers (randomly generated)

- Long Division with Money (randomly generated)

### Graded Long Division Worksheets

We have a range of printable long division worksheets.

Below are some links to our long division worksheets which are carefully graded and created individually.

Using these sheets will help your child to:

- divide by a range of numbers, including decimals;
- use their division fact knowledge to work out related division facts.

- Long Division Worksheets 3rd Grade

- 4th Grade Long Division Worksheets

- Long Division of Decimal Numbers

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Our calculator hub page contains links to all of our calculators!

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