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Understand the Remainder Formula & Find the Remainder of A Number


In this article, you will learn the remainder formula and how to calculate the remainder of two numbers when they are divided.

What is Remainder?

The number left behind after division two numbers is called the remainder. The number that is divided is known as the dividend, and the number that divides the dividend is the divisor. If a number is completely divisible by the divisor, then the remainder is zero. But if it is not completely divisible by the divisor, there will be a number left behind. For example, when 7 is divided by 3, the number 7 is not completely divisible by 3. Then, the number 1 will be left, which is its remainder.

Remainder Formula

The remainder has four parts. These are;

  • Dividend
  • Divisor
  • Quotient
  • Remainder

A dividend is a number that is divided, a divisor is a number that divides the dividend, and the resulting answer is the quotient. The quotient formula for the number that is completely divided by a divisor is,


The quotient and remainder formula for the dividend that does not completely divide by a divisor is,


If you want to find remainder, you can write the about formula as,

remainder formula
remainder formula

How to Find the Remainder in Division?

Finding the remainder of a number is an easy method. We just need a number and divide it by its divisor. For example to divide 12 by 5, you can perform the following steps to find the remainder of a number.

  1. Divide 12 by 5 such as the nearest multiple is 2.
  2. $$12\;÷\;5\;=\;2$$
  3. Since 5×2 = 10. Now by using remainder formula,
$$\text{Remainder}\;=\;12\;-(5\;×\;2)$$ $$\text{Remainder}\;=\;12\;-\;10\;=\;2$$

Let’s discuss the remainder formula in an example.

how to find remainder
how to find remainder

FAQ’s on Remainder Formula

What is the Remainder Method?

It is a method of finding the remaining number that is left behind by division of two numbers. This remaining number is known as remainder.

What is the Formula of Division with Remainder?

The remainder formula of division is,


What is the Remainder of 21 Divided by 7?

When the number 21 is divided by 7, the quotient is 3. The number 7 completely divides 21 and there is zero remainder.

Sarah Taylor

Last updated: September 09, 2020

I am a professional Chemist/Blogger & Content Writer. I love to research chemistry topics and help everyone learning Organic & Inorganic Chemistry and Biochemistry. I would do anything to spend vacations on a Hill Station.