Quotient and Remainder Calculator

Enter the dividend and divisor to calculate the quotient (integer division) and remainder.

Calculate the Quotient and Remainder

Quotient

Remainder

What Are Quotient and Remainder?

In mathematics, when one integer (the dividend) is divided by another integer (the divisor), the result consists of a quotient and a remainder. The quotient is the integer result of the division. The remainder is the leftover value after division. The relationship between these elements is expressed by the formula: \( Dividend = Divisor \times Quotient + Remainder \) Additionally, the remainder must always be less than the divisor.

How to Calculate the Quotient and Remainder?

  1. Define the Dividend and Divisor: The dividend is the number to be divided, and the divisor is the number by which the dividend is divided. For example, in \( a \div b \):
  2. Perform Integer Division:

    Quotient: Divide the dividend by the divisor and round down to the nearest whole number.

    Remainder: Subtract the product of the quotient and the divisor from the dividend. \( Remainder = Dividend - Divisor \times Quotient \)

Examples

Example 1: Dividend = 17, Divisor = 5. Find the quotient and remainder.

Solution:

Calculate the Quotient:

\( Quotient = \lfloor \frac{17}{5} \rfloor = 3 \)

Calculate the Remainder:

\( Remainder = 17 - (5 \times 3) = 17 - 15 = 2 \)

Example 2: Dividend = 1365, Divisor = 43. Find the quotient and remainder.

Solution:

Calculate the Quotient:

\( Quotient = \lfloor \frac{1365}{43} \rfloor = 31 \)

Calculate the Remainder:

\( Remainder = 1365 - (31 \times 43) = 1365 - 1333 = 32 \)

Example 3: Dividend = 100, Divisor = 6. Find the quotient and remainder.

Solution:

Calculate the Quotient:

\( Quotient = \lfloor \frac{100}{6} \rfloor = 16 \)

Calculate the Remainder:

\( Remainder = 100 - (6 \times 16) = 100 - 96 = 4 \)