Remainder Formula

The remainder formula is used to find the number left over after one number is divided by another. In a division problem, the four main parts are the dividend, divisor, quotient, and remainder. These values are connected by a simple division formula.

What Is the Remainder Formula?

The basic division formula is:

Dividend = (Divisor × Quotient) + Remainder

To find the remainder, rearrange the formula:

Remainder = Dividend − (Divisor × Quotient)

For example, if 23 is divided by 4, the quotient is 5 and the remainder is 3:

23 = (4 × 5) + 3

Therefore, the remainder is 3.

Parts of a Division Problem

Understanding the four parts of division makes the remainder formula easier to use:

Dividend: The number being divided.

Divisor: The number by which the dividend is divided.

Quotient: The whole-number result of the division.

Remainder: The amount left after the division is completed.

How to Find the Remainder

You can find a remainder by following these simple steps:

1. Divide the dividend by the divisor and find the whole-number quotient.

2. Multiply the divisor by the quotient.

3. Subtract the result from the dividend.

For example, find the remainder when 47 is divided by 5:

47 ÷ 5 = 9 with a remainder.

Now multiply:

5 × 9 = 45

Subtract:

47 − 45 = 2

So, the remainder is 2.

Remainder Formula Example

Suppose you want to find the remainder when 68 is divided by 7.

The quotient is 9 because 7 × 9 = 63.

Using the remainder formula:

Remainder = 68 − (7 × 9)

Remainder = 68 − 63

Remainder = 5

Therefore, 68 divided by 7 gives a quotient of 9 and a remainder of 5.

Important Rule of Remainder

For whole-number division, the remainder must always be less than the divisor. If the remainder is equal to or greater than the divisor, the division has not been completed correctly.

For example, in 29 ÷ 5, the remainder is 4, and 4 is less than 5. Therefore, the result is valid.

When the Remainder Is Zero

If a number can be divided exactly by another number, there is no amount left over. In this case, the remainder is zero.

For example:

36 ÷ 6 = 6

Using the formula:

36 − (6 × 6) = 0

So, the remainder is 0. This is called exact division.

Remainder and Modulo

The remainder is also commonly represented by the modulo operator % in programming and by mod in mathematics.

For example:

29 mod 5 = 4

This means that the remainder after dividing 29 by 5 is 4.

Remainder Formula in Short

The most important formula to remember is: