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Long Division Calculator with Remainders

Long Division with Remainders


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Calculator Use

Divides two whole integers, a dividend and a divisor, and expresses the answer as a whole number quotient, along with a whole number remainder. This is one of two long division methods and is simpler than producing a quotient with a decimal. You can practice your math problems then use this calculator to see how to do the long division and check against your answers.

To work with integers and decimals use our Long Division with Decimals Calculator.

Parts of Division

For the division problem 487 ÷ 32 = 15 R 7, 487 is the dividend, 32 is the divisor, 15 is the quotient and 7 is the remainder.

drawing of long division with parts of division: dividend, divisor, quotient, remainder

How to do Long Division With Remainders

From the example above, let's say we wanted to divide 487 by 32, showing our work. How would we do it?

Long Division
Explanation
Equations
step 1 long division 487 divided by 32
We set up our problem with the long division symbol or the long division bracket. Put the dividend on the inside and the divisor on the outside, left.
 
step 1 long division 487 divided by 32
Divide the first number of the dividend by the divisor. You can note the remainder but ignore it for now.
4 ÷ 32 = 0
with a remainder of 4
step 2 long division 487 divided by 32
The whole number result, 0, is placed on top to start the quotient. That number is then multiplied by the divisor. The result is placed under the number we just divided into.
32 * 0 = 0
step 3 long division 487 divided by 32
Next, subtract the bottom number from the top.
4 - 0 = 4
step 4 long division 487 divided by 32
Next, we bring down the next number of the dividend.
48
step 5 long division 487 divided by 32
We now divide this number (48) by the divisor (32). Again, You can note the remainder but ignore it for now.

Note that you could skip all of the previous steps with zeros and jump straight to this one if you realize how many digits in the dividend you need to get your first non-zero value in the quotient.  In this case you would divide 32 into 48 straight away.
48 ÷ 32 = 1
with a remainder of 16
step 6 long division 487 divided by 32
The whole number result (1) of this equation is placed in the second position of the quotient. Like the first go around, we then multiply that number by the divisor. Again, the result is placed under the number divided into.
32 * 1 = 32
step 7 long division 487 divided by 32
Subtract the product, 32, from the number above it.
48 - 32 = 16
step 8 long division 487 divided by 32
Bring down the next number from the dividend.
167
step 9 long division 487 divided by 32
Divide this number (167) by the divisor (32). See a pattern emerging?
167 ÷ 32 = 5
with a remainder of 7
step 10 long division 487 divided by 32
The whole number result (5) of this equation is placed in the next position of the quotient. Just like before, multiply that number by the divisor. Again, the result is placed under the number divided into.
32 * 5 = 160
step 11 long division 487 divided by 32
Subtract the result from the number above
167 - 160 = 7
step 11 long division 487 divided by 32
As 7 is less than 32 it is the amount left over and is the remainder. The quotient is 15 and the remainder is 7. We're all done.
487 ÷ 32 = 15
with a remainder of 7

For longer dividends, we would simply continue repeating these steps until every digit is brought down from the divdend.

Further Reading

At Ask Dr. Math you can find Instructions for Long Division for simple and more advanced long division problems.

Math is Fun also provides a step-by-step process for long division with Long Division with Remainders.



 

Cite this content, page or calculator as:

Furey, Edward "Long Division Calculator with Remainders"; from http://www.calculatorsoup.com - Online Calculator Resource.

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