Welcome to the long division calculator, the tool that helps you understand how to do long division with decimals. Read on to learn how to solve long division problems, and how to deal with long division with remainders. You can also find a long division example, complete with thoroughly explained long division steps.
Long division with remainders
As we want to learn how to do long division, let's start with basics - definitions.
Typically, we want to find a result, which is the ratio of two numbers. These two numbers are a dividend (not to be confused with dividend in finance) and a divisor. We can also write it as:
result = dividend / divisor.
We can write the result in various forms: as a fraction, a decimal (converted from the fraction), or as a combination of two numbers, a quotient, and a remainder. The latter is the essence of long division problems.
If you want to leave your result in the fractional form, you might find our ratio calculator quite helpful: it makes simplifying ratios fast and easy!
As a special case, if you want to determine the divisibility of a positive integer by 3 or 9, you can directly use the digit sum property to figure it out!
How to do long division with decimals?
The whole process is relatively simple as you have to repeat the long division steps:
As we are going to divide each part of the dividend on its own, we need to break it up. Begin by looking at how many digits your divisor has. This is how many digits we take from the left hand side of the dividend to stat working with. For example, is we are dividing 378 by 14, we will look at the 37 part of 378. We will call the numbers we take
n₁is smaller than the divisor, take the next digit from the dividend too.
Divide this value by the divisor, and round the result down to the nearest whole number. This is the first digit of the quotient.
Multiply that digit by the divisor. Let's call this
n₂. We usually receive some remainder.
With this new number, write the next digit to the right from the dividend (step 1) to the right of this value, which is our new
Continue these long division steps until you run out of digits in the dividend.
When you use the last digit from the dividend, and the difference
n₁ - n₂yields a non-zero value, that's the final remainder
You may continue by writing down further trailing zeros to obtain greater precision, and to have more significant figures. But be careful, sometimes it never ends, like for recurring decimals!
By the way, if you are interested in getting only the remainder, you can use a modulo operator because the equality
dividend mod divisor = remainder is always true.
Long division example with steps
As we've already learned the theory, let's take try to solve a particular long division example and see how our long division calculator works. In this case, let's see how to do long division of
Take the first two digits from the dividend,
65. Divide this value by
31, and round it down to the whole number, which gives us
2. Write it above as the first digit of the quotient.
31, which is
62. Write it just below the
65from the dividend. Subtract these two numbers:
65-62 = 3. That's the first digit of a new value.
Write down the next digit from the dividend,
3. Together these made
31fits only once in
33, so the next digit of the quotient is
Next, the difference
33-31 = 2and the next digit from the dividend (
2) form a new number,
Before we continue with division, we can see that
22is lower than
31, so we can write
0as the next digit in the quotient and write down another digit from the dividend, which gives us
31and rounding it down to the whole number gives us
7- the last digit of the quotient.
Then, the final standard step is
7*31 = 217, and
221-217 = 4.
As we run out of digits, and don't want to perform long division with decimal digits, these are our final results: the quotient equals
2107, and the remainder is
Alternatively, we can write
65321 / 31 = 2107 r 4
How to use the long division calculator?
The only thing you have to do is to input two values - the dividend and the divisor. And that's all! Our long division calculator will do the rest.
You can see a short answer - the quotient and the remainder, but also you can find how to do long division with all the steps.
Long division with remainders has never been so simple! Now, take up the challenge and try to solve some long division problems yourself.
💡 Want to learn how to handle complex mathematical problems that involve more than one arithmetic operation? Check our distributive property calculator.
What is long division?
In mathematics (more precisely: in arithmetic), long division is an algorithm for dividing large (multi-digit) numbers. Although long division may seem complicated at first, it, in fact, simplifies the division problem you're facing by breaking it down into a series of easier divisions.
How do I lay out long division?
The long division layout is pretty straightforward. First, write down the dividend and draw a line over it. Then write down the divisor to the left of the dividend and separate these two numbers with a vertical bar
| or a right parenthesis
How do I check the result of long division?
It's always a good idea to verify the result of long division. Simply multiply the divisor by the quotient and add the remainder - have you obtained the dividend? If so, you've solved the long division problem correctly, congratulations! If not, go again very carefully through the long division algorithm to catch the error. Good luck!
What are the 5 steps of long division?
The five steps that summarize the algorithm of long division are the following:
- Bring down; and
- Repeat or find the remainder.