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Remainder Calculator

Created by Bogna Szyk and Wojciech Sas, PhD
Reviewed by Steven Wooding and Jack Bowater
Last updated: Jan 18, 2024


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.

🙋 If you want to particularly learn how to perform other related mathematical operations, you can separately check our long division calculator, our multiplication calculator, or our subtraction calculator.

Dividend, divisor, quotient, and remainder

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

an=q+rn,\frac{a}{n} = q +\frac{r}{n},

Where:

  • aa — Initial number you want to divide, called the dividend;
  • nn — Number you divide by; it is called the divisor;
  • qq — Result of division rounded down to the nearest integer; it is called the quotient; and
  • rrRemainder 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 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.

🔎 If the remainder is zero, then we say that aa is divisible by nn. To learn more about this concept, check out Omni's divisibility test calculator.

How to calculate the remainder

  1. Begin by 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 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 eighteen of your friends, but only 15 friends showed up, you’d have 3 doughnuts left. And how much money did you have left after buying the doughnuts?

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.

FAQ

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 left that doesn’t entirely 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 2 ways of writing a remainder: with an R and as a fraction. For example, 821 divided by 4 would be written as 205 R 1 in the first case, 205 1/4 in the second.

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.
Bogna Szyk and Wojciech Sas, PhD
Division with remainder formula.
Division with remainder example.
Input two numbers
Dividend
Divisor
Result
Quotient
Remainder
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