Long Division Calculator
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
n₁
. 
If
n₁
is 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
. 
Subtract
n₁
andn₂
. 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
n₁
. 
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  n₂
yields a nonzero 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 65321
and 31
:

Take the first two digits from the dividend,
65
. Divide this value by31
, and round it down to the whole number, which gives us2
. Write it above as the first digit of the quotient. 
Multiply
2
by31
, which is62
. Write it just below the65
from the dividend. Subtract these two numbers:6562 = 3
. That's the first digit of a new value. 
Write down the next digit from the dividend,
3
. Together these made33
. 
31
fits only once in33
, so the next digit of the quotient is1
. 
Next, the difference
3331 = 2
and the next digit from the dividend (2
) form a new number,22
. 
Before we continue with division, we can see that
22
is lower than31
, so we can write0
as the next digit in the quotient and write down another digit from the dividend, which gives us221
. 
Dividing
221
by31
and rounding it down to the whole number gives us7
 the last digit of the quotient. 
Then, the final standard step is
7*31 = 217
, and221217 = 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 is4
. 
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.