Remainder Calculator (2024)

🙋 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.

Where:

• $a$a — Initial number you want to divide, called the dividend;
• $n$n — Number you divide by; it is called the divisor;
• $q$q — Result of division rounded down to the nearest integer; it is called the quotient; and
• $r$r — 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 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.

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 😀

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.

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!

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.

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.

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.