Long division calculator

The usefulness of long division

Long division is a method used to systematically divide large numbers. Many people will remember learning it in school—bent over their notebooks, pencil in hand, dividing, multiplying, subtracting, bringing down the next digit—step by step. While it might seem old-fashioned today, long division remains an important foundation in math education.

That’s because it’s not just about finding the answer, but about understanding the process. Long division teaches children to approach problems patiently and methodically. It breaks a big problem into a series of smaller, manageable calculations. Along the way, students develop a better sense of number relationships—understanding how many times one number fits into another—which later helps with fractions, percentages, and ratios.

To perform long division well, it’s essential to know your multiplication tables thoroughly. Calculators are typically not allowed when solving these types of problems, so having this knowledge is crucial. And knowing how to do long division can also come in handy when you need to divide two numbers and don’t have a calculator nearby.

How to do a long division

The long division algorithm commonly used today was introduced by English mathematician Henry Briggs (1561–1630). While calculators and computers are now the go-to tools for solving division problems, the long division method remains a valuable technique for performing multi-digit division by hand. This method works step by step from left to right across the dividend, subtracting the largest possible multiple of the divisor at each stage. These multiples form the digits of the quotient, while any amount left over is known as the remainder. In long division, the larger number being divided is called the dividend, the number you divide by is the divisor, and the answer you get is the quotient.

We will now show you how to do long division using three examples.

• Example 1: Long division without remainder
• Example 2: Long division with remainder
• Example 3: Long division with decimal number (add extra zero)

Example 1: Long division without remainder

Suppose you want to divide the number 156 by 4. You do this using long division as follows:

1. Write it down neatly
   Write the divisor (4) to the left of the bracket and the dividend (156) to the right under the bracket.
   

   4

   1

   5

   6

2. Start with the first number
   Look at the first number of 156, which is 1. Ask yourself: How many times does 4 fit into 1? It doesn't, because the number 4 is bigger than 1, so we take the next number (5) and look at the first two numbers together: 15.

   4

   1

   5

   6

3. Divide the number
   How many times does 4 go into 15? That is possible 3 times (4 x 3 = 12). We write the 3 above the 5 above the bracket. We put the 12 under the 15 and subtract it (15 - 12 = 3) which leaves us with 3:

   		3
   4	1	5	6
   	1	2
   		3

4. Take the next number
   Now we take the 6 from 156 down, next to the 3. Now we have 36.

   		3
   4	1	5	6
   	1	2
   		3	6

5. Divide again
   How many times does 4 go into 36? That is exactly 9 times (4 x 9 = 36). Write the 9 above the bracket after the 3. We put the 36 under the 36 and subtract it (36 - 36 = 0) which leaves us with 0.

   		3	9
   4	1	5	6
   		3	6
   		3	6
   			0

6. Read the answer
   Above the bracket is now 39. That is the answer: 156 ÷ 4 = 39

In this example, the division works out nicely, because at the end we have 0 left. If there is something left that you can no longer divide, that is called a remainder.

Long division with remainder

We will now divide the number 318 by 12 step by step. Using long division, you do this as follows:

1. Write it down neatly as long division
   Write 318 right below the bracket and put the number we are dividing by, in this case 12, in front of the bracket again:
   

   1

   2

   3

   1

   8

2. Start with the first number
   We first look at the first number of 318 again, which is 3. 12 does not fit 3, because the number 12 is greater than 3. We therefore take the next number (1) and now look at the first two numbers together: 31.

   1

   2

   3

   1

   8

3. Divide the number
   How many times does 12 fit into 31? The number 12 fits into 31 twice (2 x 12 = 24). We write the 2 after the last slash and put 24 under 31. Then we subtract 24 from 31, leaving 7 (31 - 24 = 7):

   			2
   1	2	3	1	8
   		2	4
   			7

4. Take the next number
   Now we take the 8 from 318 down and put it next to the 7. Now we have 78.

   			2
   1	2	3	1	8
   		2	4
   			7	8

5. Divide again
   Now see how many times 12 fits into 78? This can be done 6 times (12 x 6 = 72). We now write the 6 behind the 2 behind the last slash. We put the 72 under the 78 and subtract it (78 - 72 = 6) which leaves us with 6.

   			2	6
   1	2	3	1	8
   		2	4
   			7	8
   			7	2
   				6

6. Read the answer
   The answer now reads 26 after the last slash. However, at the end of long division we have 6 left. If there is something left that you can no longer divide, we call that the remainder. The result of this sum using long division is then, for the sake of completeness, 26 remainder 6.

Example 3: Long division with decimal number (add extra zero)

Let's go back to the example above, where we had a remainder of 6. We will now try to get rid of the remainder by continuing the long division. We do this by adding an extra zero after the number to be divided:

1. Add an extra 0 after the number to be divided
   We continue where we left off in the previous example and now add a 0 after the number to be divided, 318. In fact, we are now dividing the number 318.0 by 12. Therefore, we now also need to place a decimal point (.) after the last digit of the result.

   			2	6
   1	2	3	1	8	0
   		2	4
   			7	8
   			7	2
   				6

2. Take the extra added 0
   We take the extra added 0 down and put it next to the 6. Now we have 60.

   			2	6
   1	2	3	1	8	0
   		2	4
   			7	8
   			7	2
   				6	0

3. Divide again
   We now look again at how many times 12 fits into 60. This can be done 5 times (12 x 5 = 60). We now write the 5 behind the decimal point of the result. We put the 60 under the 60 and subtract it (60 - 60 = 0) which leaves us with 0.

   			2	6	5
   1	2	3	1	8	0
   		2	4
   			7	8
   			7	2
   				6	0
   				6	0
   					0

4. Read the answer
   The answer now reads 26.5 after the last slash. By adding an extra 0, the remainder has disappeared.

Sometimes you will need to add more zeros to avoid a remainder. However, some divisions will always have a remainder. Adding extra zeros will make your answer more accurate.

Long Division: more than just getting the answer

We learned that long division is a step-by-step method for dividing large numbers and helps us understand how division really works. It’s still taught in schools because it builds important math skills like number sense and problem-solving. With this online calculator, you can easily enter your numbers and see the full long division worked out for you. Use the long division calculator to practice and understand dividing large numbers.