Long Division Calculator

Perform long division with remainder, decimal result, and a detailed step-by-step process.

Enter Your Numbers

Result

Quotient
--
Dividend --
Divisor --
Whole Quotient --
Remainder --
Decimal Result --
Verification --
Dividend / Divisor = Quotient remainder R

Step-by-Step Solution

Understanding Long Division

Long division is a standard arithmetic method for dividing large numbers by hand. It breaks the division process into a series of simpler steps involving dividing, multiplying, subtracting, and bringing down digits. This method is taught in elementary school and remains a fundamental mathematical skill.

The process works by dividing the dividend (the number being divided) by the divisor (the number you divide by) one digit at a time, working from left to right, to find the quotient (the result) and any remainder.

Key Terms in Long Division

Dividend

The number being divided. It goes inside the division bracket.

Example: In 156 / 12, 156 is the dividend

Divisor

The number you are dividing by. It goes outside the division bracket.

Example: In 156 / 12, 12 is the divisor

Quotient

The result of the division. It is written above the division bracket.

Example: 156 / 12 = 13, quotient is 13

Remainder

The amount left over when division is not exact.

Example: 157 / 12 = 13 R 1

How Long Division Works

The Division Algorithm

Long division follows a repeating cycle of four operations, often remembered by the mnemonic Divide, Multiply, Subtract, Bring Down:

  1. Divide: Determine how many times the divisor goes into the current portion of the dividend.
  2. Multiply: Multiply the divisor by the quotient digit you just found.
  3. Subtract: Subtract the product from the current portion of the dividend.
  4. Bring Down: Bring down the next digit of the dividend and repeat the process.

Dealing with Remainders

When the division is not exact, you have two options: express the result with a remainder (e.g., 17 / 5 = 3 R 2), or continue the division into decimal places by adding a decimal point and zeros to the dividend.

Practical Applications

Long division is used in everyday situations such as splitting bills evenly among friends, calculating unit prices when shopping, converting between measurement units, and understanding rates and ratios. It is also the foundation for more advanced mathematical operations like polynomial division and modular arithmetic.

Tips for Accurate Long Division

  • Always estimate the quotient digit carefully to avoid overshooting.
  • Keep your columns aligned to prevent arithmetic errors.
  • Verify your answer by multiplying the quotient by the divisor and adding the remainder.
  • Practice with smaller numbers before tackling larger ones.
  • Use the remainder to express the result as a mixed number if needed.