Remainder Formula

The remainder is the number or value that is left when the dividend is not completely divisible by the divisor. The remainder formula helps in the calculation of the remainder obtained after the division operation between any two values. The division operation in terms of operands can be represented as:

Dividend = Divisor × Quotient + Remainder

What is the Remainder Formula?

The general formula to calculate the remainder is given as:

Examples Using Remainder Formula

Example 1: What is the remainder when 3723 is divided by 23?

Solution:     

To find: Remainder

Given: Dividend = 3723 and Divisor = 23

By long division:

Hence, Remainder = 20

Verification:

Using Remainder Formula,

Dividend = Divisor × Quotient + Remainder

3723 = 23 × 161 + 20

3723 = 3703 + 20

3723 = 3723

Since we have the same values on both sides, our answer is correct.

Answer: Remainder = 20

Example 2: A number when divided by 25 leaves remainder 4 and quotient as 11. Find that number.

Solution:     

To find: Dividend (number)

Given: 

Divisor = 25

Quotient = 11

Remainder = 4 

We know,

Dividend = Divisor × Quotient + Remainder

= 25 × 11 + 4

= 279                                                                                                                                                                                                                         

Answer: Required number = 279