Long Division Calculator

About Long Division Calculator

The Long Division Calculator solves any division problem and shows you the complete step-by-step process, exactly the way you would work it out on paper. Enter a dividend and divisor, and instantly see the quotient, remainder, and full decimal expansion with an animated visual bracket layout. It is an ideal learning companion for students and a quick verification tool for anyone who needs to double-check division results.

What Is Long Division?

Long division is the standard algorithm for dividing multi-digit numbers by hand. Unlike simple mental math, long division breaks the problem into manageable steps that process one digit at a time. It was formalized in European mathematics during the 15th century and remains one of the most important arithmetic skills taught in schools worldwide.

Parts of a Division Problem

How to Use This Calculator

1. Enter the dividend: Type the number being divided into the first input field. For example, enter 7452.
2. Enter the divisor: Type the number you are dividing by into the second field. For example, enter 12.
3. Set decimal places (optional): Adjust how many decimal places to compute if the division does not come out evenly. The default is 10.
4. Click "Solve Division": View the full step-by-step solution with an animated bracket layout, quotient, remainder, decimal expansion, and verification.

The Long Division Algorithm Step by Step

Here is how long division works, using 845 ÷ 6 as an example:

1. Divide: Look at the first digit of the dividend (8). How many times does 6 go into 8? Answer: 1 time. Write 1 as the first quotient digit.
2. Multiply: 1 × 6 = 6. Write 6 below the 8.
3. Subtract: 8 − 6 = 2.
4. Bring down: Bring down the next digit (4) to get 24.
5. Repeat: 6 goes into 24 exactly 4 times. Write 4 as the next quotient digit. 4 × 6 = 24. Subtract: 24 − 24 = 0.
6. Bring down: Bring down the last digit (5) to get 5.
7. Repeat: 6 goes into 5 zero times, remainder 5. The quotient is 140 remainder 5, or 140.833...

Understanding Repeating Decimals

When a division does not terminate (the remainder never reaches zero), the decimal digits eventually begin to repeat. This happens because there are only a finite number of possible remainders (0 through divisor−1). Once a remainder repeats, the same sequence of digits will recur.

Examples:

• 1 ÷ 3 = 0.3 (the digit 3 repeats forever)
• 1 ÷ 7 = 0.142857 (six-digit repeating cycle)
• 5 ÷ 6 = 0.83 (non-repeating part "8", then "3" repeats)

This calculator detects repeating patterns automatically and shows them with an overline bar notation.

Frequently Asked Questions

What is long division?

Long division is a standard procedure for dividing multi-digit numbers by hand. It breaks the problem into a series of easier steps by working through the dividend one digit at a time, finding how many times the divisor fits, subtracting, and bringing down the next digit.

What are the parts of a division problem?

A division problem has four parts: the dividend (the number being divided), the divisor (the number you divide by), the quotient (the result), and the remainder (what is left over). The relationship is: Dividend = Divisor × Quotient + Remainder.

What is a repeating decimal?

A repeating decimal is a decimal number where one or more digits repeat infinitely. For example, 1 divided by 3 equals 0.333... (the digit 3 repeats forever). This is written as 0.3 with a bar over the 3. Repeating decimals occur when the remainder in long division starts cycling.

How do I check if my long division answer is correct?

Multiply the quotient by the divisor and add the remainder. If the result equals the dividend, your answer is correct. Formula: Divisor × Quotient + Remainder = Dividend.

Can this calculator handle decimal dividends or divisors?

Yes. When you enter decimal numbers, the calculator automatically scales both numbers to integers by multiplying by the appropriate power of 10, then performs the division. For example, 12.5 ÷ 2.5 becomes 125 ÷ 25.

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