Remainder Calculator

By Bogna Szyk and Wojciech Sas, PhD candidate
Last updated: Feb 08, 2021

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.

Dividend, divisor, quotient and remainder

When you perform division, you can typically write down this operation in the following way:

a/n = q + r/n


  • a is the initial number you want to divide, called the dividend.
  • n is the number you divide by; it is called the divisor.
  • q is the result of division rounded down to the nearest integer; it is called the quotient.
  • r is the remainder of this mathematical operation.

When performing division with our calculator with remainders, it is important to remember that all of these values must be integers. Otherwise the result will be correct in the terms of formulas, but will not make mathematical sense.

Make sure to check our modulo calculator for a practical application of the calculator with remainders.

How to calculate the remainder

  1. Begin with writing down your problem. For example, you want to divide 346 by 7.
  2. Decide on which of the numbers is the dividend, and which is the divisor. The dividend is the number that the operation is performed on - in this case, 346. The divisor is the number that actually "does the work" - in this case, 7.
  3. Perform the division - you can use any calculator you want. You will get a result that most probably is not an integer - in this example, 49.4285714.
  4. Round this number down. In our example, you will get 49.
  5. Multiply the number you obtained in the previous step by the divisor. In our case, 49 * 7 = 343.
  6. Subtract the number from the previous step from your dividend to get the remainder. 346 - 343 = 3.
  7. You can always use our calculator with remainders instead and save yourself some time :)


How do you solve Chinese remainder theorem problems?

  1. Make sure you have an unknown equal to two or more different modulos, e.g. x=d mod a, e mod b & f mod c.
  2. Check that all modulos have the same greatest common divisor.
  3. Multiply each modulo by all but one other modulo, until all combinations are found. For the above modulos, this would be: bc, ac, a*b.
  4. Divide each number by the modulo that it is missing. If it equals the remainder for that modulo, e.g. (b*c)/a = d, leave the number as is.
  5. If the remainder is not that for the modulo, use trial and error to find a positive integer to multiply the number by so that step 4 becomes true.
  6. Add all numbers together once step 4 is true for all combinations.

What are some remainder tricks?

It's useful to remember some remainder shortcuts to save you time in the future. First, if a number is being divided by 10, then the remainder is just the last digit of that number. Similarly, if a number is being divided by 9, add each of the digits to each other until you are left with one number (e.g., 1164 becomes 12 which in turn becomes 3), which is the remainder. Lastly, you can multiply the decimal of the quotient by the divisor to get the remainder.

How do I interpret the remainder?

Learning how to calculate the remainder has many real world uses, and is something that school teaches you that you will definitely use in your everyday life. Let’s say you bought 18 doughnuts for your friend, but only 15 of them showed up, you’d have 3 left. Or how much money did you have left after buying the doughnuts? If the maximum number of monkeys in a barrel is 150, and there are 183 monkeys in an area, how many monkeys will be in the smaller group?

How do you turn a remainder into a decimal?

  1. Set up your division, adding a decimal place followed by a zero after the dividend’s one’s column (if your dividend is already a decimal, add an additional zero to the end).
  2. Perform the division as normal, until you are left with the remainder.
  3. Instead of writing the remainder after the quotient, move the remainder above the additional zero you placed.
  4. If there is a remainder from this division, add another zero to the dividend and add the remainder to that.
  5. Continue in this fashion until there is either: no remainder, the digit or digits repeat themselves endlessly, or you reach a desired degree of accuracy (3 decimal places is usually okay).
  6. The result after the decimal place is the remainder as a decimal.

What is the quotient and the remainder?

The quotient is the number of times a division is completed fully, while the remainder is the amount that is left that doesn’t fully go into the divisor. For example, 127 divided by 3 is 42 R 1, so 42 is the quotient and 1 is the remainder.

How do you write a remainder as a fraction?

Once you have found the remainder of a division, instead of writing R followed by the remainder after the quotient, simply write a fraction where the remainder is divided by the divisor of the original equation. It's that easy!

How do you write remainders?

There are 3 ways of writing a remainder: with an R, as a fraction, and as a decimal. For example, 821 divided by 4 would be written as 205 R 1 in the first case, 205 1/4 in the second, and 205.25 in the third.

What is the remainder when 26 is divided by 6?

The remainder is 2. To work this out, find the largest multiple of 6 that is less than 26. In this case it’s 24. Then subtract the 24 from 26 to get the remainder, which is 2.

What is the remainder when 599 is divided by 9?

The remainder is 5. To calculate this, first divide 599 by 9 to get the largest multiple of 9 before 599. 5/9 < 1, so carry the 5 to the tens, 59/9 = 6 r 5, so carry the 5 to the digits. 59/9 = 6 r 5 again, so the largest multiple is 66. Multiply 66 by 9 to get 594, and subtract this from 599 to get 5, the remainder.

How do I calculate the remainder of 24 divided by 7?

  1. Subtract 7 from 24 repeatedly until the result is less than 7.
  2. 24 minus 3 times 7 is 3.
  3. The number that is left, 3, is the remainder.
  4. This can be expressed as 3/7 in fractional form, or as 0.42857 in decimal form.
Bogna Szyk and Wojciech Sas, PhD candidate
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