Remainder Calculator (2024)

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Dividend, divisor, quotient, and remainderHow to calculate the remainderHow do I interpret the remainder?What are some remainder tricks?FAQs

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},na=q+nr,


  • aaa — Initial number you want to divide, called the dividend;
  • nnn — Number you divide by; it is called the divisor;
  • qqq — Result of division rounded down to the nearest integer; it is called the quotient; and
  • rrrRemainder 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 aaa is divisible by nnn. 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.


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.
Least Common Multiple CalculatorAbsolute Value Calculator
Remainder Calculator (2024)


What is the easiest way to calculate a remainder? ›

How to Find the Remainder?
  1. Step 1: Divide the dividend by the divisor using integer division, ignoring any remainder.
  2. Step 2: Multiply the divisor by the quotient obtained in step 1.
  3. Step 3: Subtract the result obtained in step 2 from the dividend.
  4. Step 4: The resulting integer is the remainder.
May 23, 2023

What is the remainder when 85x87x89x91x95x96 is divided by 100? ›

We have to find the remainder. Therefore, the remainder when 85 x 87 x 89 x 91 x 95 x 96 is divided by 100 is 0.

Can the remainder be greater than the answer? ›

The remainder will always be less than the divisor. If your remainder is greater than your divisor, that means there is still more division you can perform, and your quotient is incomplete. If the remainder is greater than the divisor, that means the divisor can still fit into the dividend another time.

What is the remainder when 7 5284 is divided by 5? ›

We can use Fermat's little theorem: 74≡1(mod5) 7 4 ≡ 1 ( mod 5 ) . Hence, 75284=74k≡1(mod5) 7 5284 = 7 4 k ≡ 1 ( mod 5 ) . Therefore the remainder is 1.

How to find remainder without dividing? ›

Another way to find the remainder is to set the x - a to term equal to 0 and then solve for x. After this, you just plug it back in to find the remainder.

What is the short trick for finding the remainder? ›

We know that when a number M is divided by another number N, and if M > N, then the remainder is calculated by subtracting the maximum possible multiple of N from M.

What is the formula for remainder? ›

One way to write the remainder is to separate the quotient and the remainder with a "R." 7/2 = Q=3 and R=1 is the formula for dividing 7 by 2. In this case, Q=3 is a quotient, and R=1 is a remainder.

What is the remainder 85 * 87 * 89 * 91 * 95 * 96 divided by 100? ›

Answer: The full product (85 × 87 × 89 × 91 × 95 × 96) is fully divisible by 100 , (which is 5x5x4). So, the remainder will be zero.

How do you divide 100 percent? ›

100% means you have 1 whole thing! So if you had 3 and were to divide it by 100%, you'd be dividing by the whole thing, which is 3. And 3 ÷ 3 = 1. So dividing something by 100% will give you that same value!

What is 100 divided evenly? ›

Thus, the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100. If we divide 100 by different numbers other than 1, 2, 4, 5, 10, 20, 25, 50 and 100, it leaves a remainder and hence, they are not the factors of 100.

What is the rule for remainders? ›

The result of the division is called a “quotient.” When the dividend is not completely divided by the divisor, the leftover value is called “remainder.” Example: Divide 25 by 6. Thus, quotient and we are left with the remainder of 1. We can write this as 25 ÷ 6 → 4 R 1 , where 4 is the quotient and 1 is the remainder.

How to calculate remainder in calculator? ›

Work the division in your calculator as normal. Once you have the answer in decimal form, subtract the whole number, then multiply the decimal value that's left by the divisor of your original problem. The result is your remainder.

How do you find the remainder function? ›

Description. r = rem( a , b ) returns the remainder after division of a by b , where a is the dividend and b is the divisor. This function is often called the remainder operation, which can be expressed as r = a - b.

Which formula is used to find the remainder? ›

Answer. Step-by-step explanation: (Dividend/division)-Quotient=remainder.

How do you work out the remainder of a decimal? ›

In this math lesson, we learn how to divide two numbers and find a decimal answer. We divide 63 by 35, first getting a remainder of 28. To obtain a decimal result, we add a zero to 63, making it 63.0, and then divide 280 by 35. The final answer is 1.8.

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