Long Division Calculator - with Steps to Solve (2024)

Enter the divisor and dividend below to calculate the quotient and remainder using long division. The results and steps to solve it are shown below.

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Result:

Full Answer:

18 R 3

Quotient:

18

Remainder:

3

Solution

18
475
-4
35
-32
3

Learn how we calculated this below

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On this page:

  • Long Division Calculator
  • How to Do Long Division with Remainders
  • Parts of a Long Division Problem
  • Steps to Calculate a Long Division Problem
  • How to get the Quotient and Remainder as a Decimal
  • How to do Long Division Without Division
  • Frequently Asked Questions
  • References

By

Long Division Calculator - with Steps to Solve (1)

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

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Reviewed by

Long Division Calculator - with Steps to Solve (2)

Ethan has a PhD in astrophysics and is currently a satellite imaging scientist. He specializes in math, science, and astrophysics.

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Cite As:

Sexton, J. (n.d.). Long Division Calculator – with Steps to Solve. Inch Calculator. Retrieved May 14, 2024, from https://www.inchcalculator.com/long-division-calculator/

How to Do Long Division with Remainders

Learning long division is a crucial milestone in understanding essential math skills and a rite of passage to completing elementary school. It strikes fear in elementary school students and parents alike.

A recent study found that the understanding of long division and fractions in elementary school is directly linked to the student’s ability to learn and understand algebra later in school.[1]

Have no fear!

Learning long division can be easy, and in just a few easy steps, you can solve any long division problem. Follow along as we break it down, but first, we need to cover the anatomy of a long division problem.

Parts of a Long Division Problem

Long Division Calculator - with Steps to Solve (3)

There are a few parts to a long division problem, as shown in the image above.

The dividend is the number being divided and appears to the right and under the division line.

The divisor is the number being divided by and appears to the left of the division line.

The quotient is the solution and is shown above the dividend over the division line. Often in long division, the quotient is referred to as just the whole number part of the solution.

The remainder is the remaining part of the solution, or what’s leftover, that doesn’t fit evenly into the quotient.

Steps to Calculate a Long Division Problem

There are a few main steps to solving a long division problem: divide, multiply, subtract, bringing the number down, and repeating the process.

Step One: Set up the Expression

The first step in solving a long division problem is to draw the equation that needs to be solved. If the problem is already in long division form, then skip along to step two.

If it’s not, this is how to draw the long division problem.

Start by drawing a vertical bar to separate the divisor and dividend and an overbar to separate the dividend and quotient.

Place the dividend to the right of the vertical bar and under the overbar. Place the divisor to the left of the vertical bar.

For example, to divide 75 by 4, the long division problem should look like this:

Long Division Calculator - with Steps to Solve (4)

Step Two: Divide

With the long division problem drawn, start by dividing the first digit in the dividend by the divisor.

You can also think about this as counting the number of times the divisor will evenly fit into this digit in the dividend.

If the divisor does not fit into the first digit an even number of times, drop the remainder or decimal portion of the result and write the whole number portion of the result in the quotient above the overline directly above the digit in the dividend.

For example, the divisor “4” goes evenly into the first digit of the dividend “7” one time, so a “1” can be added to the quotient above the 7.

Long Division Calculator - with Steps to Solve (5)

Step Three: Multiply

The next step is to multiply the divisor by the digit just added to the quotient. Write the result below the digit in the dividend.

This step forms the part of the expression for the next step.

Continuing with our example, multiplying the divisor “4” by “1”, which we found in the previous step, equals “4”. So, add a “4” below the first digit in the dividend.

Long Division Calculator - with Steps to Solve (6)

Step Four: Subtract

Now, add a minus sign “-” before the number added in the previous step and draw a line below it to form a subtraction expression.

Continuing the example above, add a “-” before the “4” and a subtraction line below it.

Long Division Calculator - with Steps to Solve (7)

Now that you have created a subtraction problem, it’s time to solve it.

To solve, subtract “7” minus “4”, which equals “3”, so write a “3” below the subtraction line.

Long Division Calculator - with Steps to Solve (8)

Note: if the resulting value of the subtraction problem is greater than the divisor, then you made a mistake in step 2 and should double-check your work.

If the long division problem has a dividend that is a single digit, then hooray, you’re done! The remaining number that is the result of the subtraction problem is the remainder, and the number above the dividend is the whole number quotient.

If more digits are remaining in the dividend, then proceed to the next step.

Step Five: Pull Down the Next Number

At this point in the process, it’s time to operate on the next number in the dividend. To do this, pull down the next digit in the dividend and place it directly to the right of the result from the subtraction problem above.

The next digit in the dividend is “5”. So, pull “5” down and write it next to the “3” found in the previous step.

Long Division Calculator - with Steps to Solve (9)

Step Six: Repeat

At this point, you might be wondering where to go from here. Repeat steps two to five until all the digits in the dividend have been pulled down, divided, multiplied, and subtracted.

When dividing, use the result of the subtraction problem combined with the pulled-down digit as the dividend and divide the divisor into it.

Continuing the examples above, divide the result of the subtraction problem and the pulled-down digit by the divisor. Thus, the next step is to divide 35 by 4. The result is “8”, so add “8” to the quotient.

Long Division Calculator - with Steps to Solve (10)

Next, multiply the quotient digit “8” by the divisor “4”, which equals 32. Add “32” to the long division problem and place a negative sign in front of it.

Long Division Calculator - with Steps to Solve (11)

Next, repeat the subtraction process, subtracting 32 from 35, which equals 3. Add a “3” below the subtraction line. Since there are no longer any remaining digits in the dividend, this is the remainder portion of the solution.

Long Division Calculator - with Steps to Solve (12)

Therefore, 75 divided by 4 is 18 with a remainder of 3. As you practice these steps, use the calculator above to confirm your answer and validate your steps solving long division problems.

How to get the Quotient and Remainder as a Decimal

If you’ve gotten this far, then you should have a good idea of how to solve a long division problem, but you might be stuck if you need to get the quotient as a decimal rather than a whole number with a remainder.

To calculate the quotient in decimal form, follow the steps above the get the whole number and remainder.

Next, divide the remainder by the divisor to get the remainder as a decimal. Finally, add the decimal to the quotient to get the quotient in decimal form.

For example, 75 ÷ 4 is 18 with a remainder of 3.

Divide 3 by 4 to get the decimal 0.75.
3 ÷ 4 = 0.75

Then, add 0.75 to 18 to get the quotient as a decimal.
0.75 + 18 = 18.75

Thus, the decimal form of 75 ÷ 4 equals 18.75.

How to do Long Division Without Division

While it defeats the purpose of actually learning how to do long division, there is technically a way to perform long division without actually doing any division. The way to do this is as follows.

Step One: Set up the Expression

Set up the long division expression the exact same way as you would normally.

Long Division Calculator - with Steps to Solve (13)

Step Two: Repeatedly Subtract the Divisor

Now, subtract the divisor from the dividend. Afterward, subtract the divisor again from the remaining value. Do this repeatedly until the remaining value is less than the divisor.

Long Division Calculator - with Steps to Solve (14)

Step Three: Count the Number of Subtractions

Finally, to find the quotient, simply count the number of times you subtracted the divisor. This is the whole number portion of the quotient, and the final remaining value is the remainder.

Long Division Calculator - with Steps to Solve (15)

Note: While this method of solving long division problems may seem easier, it is often very impractical to do so. For example, in the above example of 75 divided by 4, you would need to repeat the subtraction 18 times!

Therefore, traditional long division is the vastly superior method.

Frequently Asked Questions

Why is long division important?

Long division is important not just because it is a tool that allows us to solve difficult division problems, but because it helps to teach logical thinking that will prepare students to excel in solving future mathematical problems.

Why do we still teach long division?

We still teach long division because it teaches students how to think logically, a valuable skill that is shown not just to improve future understanding of algebraic concepts, but also to help solve problems in all aspects of their lives.

How do you check a long division answer?

Just like subtraction is the opposite of addition, multiplication is the opposite of division. Therefore, to check a long division answer, multiply the quotient by the divisor, and if it equals the dividend, then the answer is correct!

Can you do long division on a calculator?

While a calculator can solve division problems, it will not list out the steps used in evaluating a long division problem, and will therefore not improve your understanding of how to perform long division.

Long Division Calculator - with Steps to Solve (2024)

FAQs

How to calculate long division step by step? ›

How to Do Long Division in Simple Steps
  1. Set up the problem. Write the dividend (845) under the division bar and the divisor (3) outside the bar.
  2. Divide. ...
  3. Multiply. ...
  4. Subtract. ...
  5. Bring down the next digit. ...
  6. Repeat the steps. ...
  7. The final answer with a remainder. ...
  8. Convert the remainder to decimal form.
Feb 6, 2024

What is 8.14 divided by 20 long division? ›

To divide 8.14 by 20, you can use long division. The first step is to write 8.14 as a whole number by moving the decimal point two places to the right, making it 814. Then, divide 814 by 20. The quotient is 40.7.

What is the quotient and remainder calculator? ›

This quotient and remainder calculator helps you divide any number by an integer and calculate the result in the form of integers. In this article, we will explain to you how to use this tool and what are its limitations. We will also provide you with an example that will better illustrate its purpose.

What is the general formula for long division? ›

Algebraic Long Method

Divide the first term of the dividend (the polynomial to be divided) by the first term of the divisor. This gives the first term of the quotient. Multiply the divisor by the first term of the quotient. Subtract the product from the dividend then bring down the next term.

How to do long division with decimals step by step? ›

Therefore, the three steps to performing long division with decimals are: 1) eliminate the decimal from the divisor, if any; 2) perform long division as usual; and 3) use the same decimal place for the quotient as in the dividend.

What is the algorithm for long division? ›

The standard algorithm for long division is a series of steps repeated in this order: divide, multiply, subtract, bring down. With the standard algorithm, we solve division problems one place value at a time.

What is 2 192 divided by 6? ›

We can observe that the remainders repeat after every 6 powers. Since 192 is divisible by 6 (192 ÷ 6 = 32), we can conclude that the remainder when 2^192 is divided by 6 is the same as the remainder when 2^6 is divided by 6, which is 2. Therefore, the remainder when 2^192 is divided by 6 is 2.

What is the remainder when 9999999925 is divisible by 9? ›

Therefore, the remainder when the number 9999999925 is divided by 9 is 7.

Is 85 * 87 * 89 * 91 * 95 * 96 is divided by 100? ›

So the full product (85 × 87 × 89 × 91 × 95 × 96) is fully divisible by 100 (which is 5x5x4). So the remainder will be zero.

What is the remainder when 123456785 is divided by 9 2? ›

After adding the digits of the number, we have, As we know that 36 is divisible by 9, so there is no remainder when 12345678 is divisible by 9.

How to do a long division step by step? ›

Long Division Steps

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor. Step 2: Then divide it by the divisor and write the answer on top as the quotient. Step 3: Subtract the result from the digit and write the difference below.

How many times does 13 go into 26? ›

13 goes into 26 twice.

How to divide large numbers quickly? ›

Another useful technique to divide large numbers mentally is to use halving and doubling, which is based on the fact that dividing by 2 is the same as multiplying by 0.5, and vice versa. For example, if you want to divide 720 by 24, you can halve both numbers until you get an easier division.

How do you find the roots using long division method? ›

Step 1: Divide the given number by divisor by identifying the suitable integer. Step 2: Multiply the divisor and integer (quotient) to get the number to be subtracted from the dividend. Step 3: Subtract the number from the dividend. Step 4: Bring down the remainder and another digit (if any) from the dividend.

What is the division formula? ›

Division Math Formula

The formula to calculate the division of two numbers is: Dividend ÷ Divisor = Quotient + Remainder. The remainder is the leftover number in the division operation. If 46 is divided by 5, we get the quotient as 9 and the remainder 1.

References

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