Long Division Calculator

How to Do Long Division Step-by-Step

Long division is a method used to divide larger numbers by breaking the calculation into smaller, repeatable steps. It is useful when a division problem cannot be solved easily using mental math or simple division facts.

The standard long division process follows four main steps: divide, multiply, subtract, and bring down. These steps are repeated until all the digits have been used, giving you the quotient and, when the division is not exact, the remainder.

The 4 Steps of Long Division

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

Long Division Example: 487 ÷ 5

Let us solve 487 divided by 5 step by step using the long division method.

Step 1: Start with 4. Since 5 is greater than 4, it cannot go into 4. Move to the first two digits and use 48. The number 5 goes into 48 nine times because 5 × 9 = 45. Write 9 in the quotient.

Step 2: Subtract 45 from 48 to find what is left.

Step 3: Bring down the next digit, 7, next to the remainder 3. This gives us 37.

Step 4: Divide 37 by 5. The number 5 goes into 37 seven times because 5 × 7 = 35. Write 7 in the quotient.

Step 5: Subtract 35 from 37. The result is 2. There are no more digits to bring down, so the division is complete.

The quotient is 97 and the remainder is 2.

Long Division With a Remainder

A remainder occurs when the divisor does not divide the dividend evenly. It is the amount left after the largest possible whole-number quotient has been found. The remainder must always be smaller than the divisor.

For example, when 23 is divided by 4, the number 4 goes into 23 five complete times. Five groups of 4 use 20, leaving 3.

You can check a division answer with a remainder by multiplying the divisor by the quotient and then adding the remainder.

Long Division With Decimals

Long division can also be used to find an exact decimal answer. If there is a remainder after all the digits of the dividend have been used, place a decimal point in the quotient and add a zero to the remainder. Continue the divide, multiply, subtract, and bring-down process until the remainder becomes zero or the required precision is reached.

For example, 15 divided by 4 gives a quotient of 3 with a remainder of 3. To continue, place a decimal point after 3 and add a zero to the remainder, making 30.

Bring down another zero to make 20. Then 4 goes into 20 five times with no remainder.

Therefore, the exact decimal answer is 3.75.

Converting a Remainder to a Decimal

A remainder can also be converted into a decimal by dividing the remainder by the divisor. For 487 ÷ 5, the whole-number result is 97 with a remainder of 2. Since 2 ÷ 5 = 0.4, the decimal result is 97.4.

The Division Algorithm

The relationship between the dividend, divisor, quotient, and remainder can be written using the division algorithm:

Using the 487 ÷ 5 example, the formula confirms the result:

Common Mistakes to Avoid

• Skipping a Step: Follow the divide, multiply, subtract, and bring-down sequence carefully.
• Starting With a Number Too Small: If the divisor is larger than the first digit, use enough digits from the dividend to form a number that the divisor can divide.
• Writing the Quotient in the Wrong Place: Each quotient digit should align with the part of the dividend being divided.
• Incorrect Subtraction: Check each subtraction before bringing down the next digit.
• Ignoring the Remainder: If the division is not exact, include the final remainder in the answer.
• Using an Invalid Remainder: The remainder must always be smaller than the divisor.

Why Use a Long Division Calculator?

A long division calculator can make multi-digit division faster and easier to check. It can provide the quotient, remainder, or decimal result and, when step-by-step calculations are supported, show how the answer was obtained rather than only displaying the final result.