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remainder Calculator

Remainder Calculator

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The free quotient and remainder calculator allow you to find the quotient and remainder after dividing the two natural numbers dividend and divisor.

In this article, we will clarify that what is quotient and remainder along with formula, how to use this long division calculator with remainder, how to find remainder (manually), and much more for the better understanding.

About Dividend, Divisor, Quotient, and Remainder

In the procedure of division, there are four important values recognized as:

  • Dividend: In any equation, the number which we divide is known as a dividend.
  • Divisor: The number by which division takes place is the divisor.
  • Quotient: The obtained result is known as quotient.
  • Remainder: The amount or leftover is the remainder.

Assume a condition: 30/8 = 3(8/6)

  • Divisor = 8
  • Dividend = 30
  • Remainder = 6
  • Quotient = 3

This long division calculator with the remainder assists students or professionals in dealing with lengthy mathematical problems with ease as it delivers precise remainders and quotients.


  • Dividend/Divisor = Quotient + Remainder/Divisor.
  • Dividend = Quotient*Divisor + Remainder

While carrying out division remembers to use this calculator with remainders instead of formula to reduce the risk of error.

About Quotient and Remainder Calculator:

Our remainder calculator assists you in process of division to find the remainder online. Whenever you will enter dividend in the first place and then divisor, it delivers non-decimal (whole number) values for quotient and reminder. Furthermore, you cannot enter the values with fractions or decimals at all. If you have to deal with the bulk of mathematical problems, then this long division calculator with remainders assists you to avoid the possibility of miscalculation.

How to Calculate The Remainder With this Remainder Calculator?

Fill in the inputs to find quotient and remainder. Our division calculator with the remainder asks you to enter Dividend represented by X and divisor represented by Y. Both values can be either negative or positive.

To Calculate Remainder and Quotient:

Decide any two numbers. Now label the one number as dividend and the other as the divisor. Follow the simple steps:


  • In the first step, you have to enter the non-decimal dividend.
  • Very next you have to enter the non-decimal divisor.
  • Hit the calculate button.


  • You will have the quotient in the form of an integer.
  • You will have the remainder in the form of an integer.

Note: To find the remainder for another calculation just hit the reset button. whereas Integer is the whole number or a non-decimal value.

How to Find Remainder?

Quotient and remainder cannot be present without calculations as they are the result of any division. If you have two values 7 and 2 and want to divide 7 by 2. In this case 7 is dividend and 2 is divisor.

  • Now perform the division manually or with the help of any ordinary calculator. You will get an answer in non-integer. In the above case, the answer will be: 3.50
  • Round off the answer and you will get 4.
  • Now apply the formula: dividend = quotient*divisor + remainder
  • Multiply the number by the divisor (quotient*divisor) In our case, 4* 2 = 8
  • Subtract the number from dividends to get the remainder (dividend – 8) in our case: 7 – 8 = -1.
  • Remainder = 1 (according to mathematical rules remainder can never be negative)

You can always use our long division calculator with remainders instead of doing it manually to save time and minimize the risk of miscalculation.

FAQ’s (Quotient, Remainder, and Long Division with Remainders)

What is the remainder?

In math, it is the leftover value after division calculation. It is a non-fraction or non-decimal number that is obtained by the division of one integer with another to produce an integer quotient. Whereas quotient is the answer to any division calculation.

What are some remainder tricks?

It’s beneficial to think of some remainder hacks to save time and effort. Some of them are explain below:

First any number is being divided by 10: 150/10 then the remainder is just the last digit of that number as in this case remainder will be 0.

If any number is being divided by 9, add each of the digits to each other until you are left with one number. This last on number will be remainder. For example, if you have a number 2354/9 then: 2+3 = 5 and 5+5 =10 and 10+4 =14 lastly 1+4 = 5. Remainder = 5.

Is zero a remainder?

When awe uses one number as a dividend and other as the divisor, the result will be “quotient” and a “remainder”. If we got zero as a remainder then it means that both the quotient and divisor are factors of the dividend. For example: if 6 is dividends and 2 is divisor then quotient will be 3 and the remainder will be 0. Our quotient (3) and divisor (2) are factors of 6.

When N is divided by 12 What is the remainder of 6?

If n = 6 + 12*k

In this case, k is representing a positive integer. Now by dividing n by 12 the answer will be 6 and recognized as remainder. The reason behind the phenomenon is that the calculation 12*k part is dividable by 12.

How do you write a remainder as a fraction?

When you find out the remainder, as an alternative R simply write a fraction where the remainder is divided by the divisor.

Example: 30/8 = 3(8/6)

In this equation remainder is 6

What is the synonym of the remainder?

It has different synonyms:

  • It is identified as a number that lefts after subtraction
  • It is the number that gives minuend when added to the subtrahend.
  • deviation, remains, conclusion, remaining, oddment, leftover, the remnant are some other names.

Can a remainder be negative?

The value of the remainder can never be negative in any case. Anyone can write the equation and use the negative number as a remainder, but according to Euclid’s division algorithm lemma, it can never be negative.

What is the remainder when 100 is divided by 11?

The remainder will be 1 when we divide 100 by 11.


  • Devisor: 11
  • Dividend: 100
  • Formula: dividend = divisor*quotient + remainder
  • Enter values: 100 = 11 * 9 +R; 99 – 100 = 1

What is the remainder of 10 divided by 3?

According to give condition that is 10/3; 3 is divisor and 10 is a dividend. The remainder will be 1.

Explanation: Apply the formula that is dividend = divisor*quotient + remainder.

10= 3*3 + R; 10-9 = 1 (remainder)

What does a remainder of 0 mean?

It means that in the process of division; our quotients and divisors are a factor of dividends. For example, if the dividend is 8 and the divisor is 4 then the remainder will be zero. Therefore, we can conclude that 2 that is a quotient and divisor 4 are the factors of 8.

What is a remainder in the long division?

When there is a lot of numbers then it will be a long division case. While doing calculation we will notice that the answer is not always going to be a whole number. In such situations, numbers will be left and recognized as remainders. In such cases, the first number of the dividend will be divided by the divisor. The integer result will be placed at the top.

What is the remainder of 5 divided by 2?

5/2 explains that 5 is the divisor and 2 is the dividend. Now you will get 2 as a quotient. Multiply it with divisor. The answer will 4 now minus the number from dividends to get the remainder. That will be 1.

What is the remainder when 121012 is divided by 12?

In this condition 121012/12; divisor is 121012 and the dividend is 12. The remainder will be 4.

Dividend is 121012 and Divisor 12.

According to formula: 121012 = 12*10084 + R

R= 121008 – 121012 = 4

What is the remainder when 8 is divided by 12?

Follow the simple formula to calculate the remainder;

Dividend = quotient*divisor + remainder

Condition is 8/12; 8 is the divisor and 12 is the dividend.

  • Divide 8 by 12 = 0.666
  • Round off the number = 1
  • Now multiply it with divisor: 8*1 = 8
  • Now subtract the number from dividend: 12-8 =
  • Remainder = 4

What is the formula of the divisor?

It is a value that divides another number. As a result, there can be a remainder and quotient. it can be represented by dividend/divisor= quotient.


Our Remainder Calculator works online as a tool that displays a value for the remainder and quotient in response to the given input. This tool makes calculations very simple and motivating. You can use it in cases of long divisions with remainders to eliminate the risk of error up to 100%. Furthermore, it is free to use so students and professionals can enhance their skills via its support and save their time by avoiding long manual division calculations.


From Wikipedia, the free encyclopedia – In mathematics, The Remainder – Integer division – Examples

From Wikipedia, the free encyclopedia – In arithmetic, a Quotient – Integer part definition – Notation – Quotient of two integers

From The Source of Mathisfun – Long Division with Remainders –All you need to know about Long Division

From the source of khanacademy – The quotient remainder theorem – Examples