Long Division Calculator

How to use this calculator

To use this calculator, follow 4 steps:

• Enter the dividend in the first input field.
• Enter the divisor in the second input field.
• Choose an output mode: quotient with remainder, exact decimal value, or full long division layout.
• Click Calculate to read the step-by-step solution.

The Long Division Calculator with Steps shows the division bracket setup, each subtraction, and every digit you bring down. For decimal inputs, the calculator rewrites the problem as an equivalent whole-number division so the workspace stays easy to read.

Background

Long division is a method that divides large numbers one digit at a time. Division is one of the four arithmetic operations, alongside multiplication, addition, and subtraction. Multiplication reverses division, so every long division problem checks against a matching multiplication. Long division breaks one large problem into a short sequence you repeat until no digits remain. The Long Division Calculator runs this sequence and prints each partial result, so the reasoning stays visible from the first digit to the final remainder or decimal point.

Enter values

To enter values, type the dividend into the first field and the divisor into the second field. The dividend is the number you divide. The divisor is the number you divide by. For 487 ÷ 32, enter 487 as the dividend and 32 as the divisor. The Long Division Calculator accepts whole numbers, decimals, and negative numbers, then returns the quotient and remainder for the pair you entered.

How this calculator works

The Long Division Calculator works through five internal actions:

• Rewrites decimal division as an equivalent whole-number division when either input carries a decimal point.
• Divides one digit at a time using the divide, multiply, subtract, and bring down sequence.
• Continues past the decimal point when a remainder exists and an exact decimal value is requested.
• Detects a repeating remainder and marks the repeating decimal solution.
• Simplifies the answer into a fraction and a mixed number where one applies.

Multiplying both the dividend and divisor by the same power of 10 leaves the quotient unchanged, so the calculator scales decimals to whole numbers without altering the result.

Formula & Relationship Used

The Long Division Calculator uses one main relationship: Dividend = Divisor × Quotient + Remainder. This identity ties all four values of a division problem together. The remainder rule fixes the range of the leftover value: 0 ≤ Remainder < Divisor. A third relationship handles decimals: multiplying the dividend and divisor by the same power of 10 produces an equivalent division with the same quotient. For 487 ÷ 32 = 15 R7, the identity confirms the answer: 32 × 15 + 7 = 487.

Components of division

A division problem has 3 main parts: the dividend, the divisor, and the quotient. The dividend is the number being divided. The divisor is the number that divides the dividend. The quotient is the result. A fourth value, the remainder, holds any leftover amount when the division is uneven.

For the division sentence 487 ÷ 32 = 15 R7:

• 487 is the dividend.
• 32 is the divisor.
• 15 is the quotient.
• 7 is the remainder.

The dividend represents the total number of objects. The divisor represents the number of groups. The quotient represents the number of objects in each group. For 8 ÷ 4 = 2, splitting 8 objects into 4 groups places 2 objects in each group.

How to perform long division?

To perform long division, identify the dividend and divisor, set up the division bracket, then repeat the long division steps until no digits remain. To divide 100 by 7, where 100 is the dividend and 7 is the divisor, write 100 inside a radicand and place 7 to the left. Divide left to right, digit by digit, and record each partial quotient above the bracket. When the divisor no longer fits into the leftover value, that value becomes the remainder, and the Long Division Calculator returns 100 ÷ 7 = 14 R2.

      
7 ) 100

How to Do Long Division

The long division steps repeat until every digit of the dividend has been used. There are 5 steps in long division: divide, multiply, subtract, bring down, and repeat.

    1
7 ) 100
   ^

Divide

Divide the smallest part of the dividend that the divisor fits into. This step produces one digit of the quotient. For 100 ÷ 7, the divisor 7 fits into 10 one time, so write 1 above the second digit.

Multiply

Multiply the quotient digit by the divisor, then write the product below the partial dividend. For the first step of 100 ÷ 7, multiply 1 by 7 to get 7, and write 7 under the 10.

Subtract

Subtract the product from the partial dividend to find the leftover value. The leftover value stays smaller than the divisor. For 100 ÷ 7, subtract 7 from 10 to get 3.

Bring Down

Bring down the next digit of the dividend and place it beside the leftover value. For 100 ÷ 7, bring down the 0 to form 30, then return to the divide step.

Repeat

Repeat the divide, multiply, and subtract steps until every digit has been brought down. For 100 ÷ 7, the divisor 7 fits into 30 four times, 4 × 7 = 28, and 30 − 28 = 2. No digits remain, so the quotient is 14 and the remainder is 2.

Long Division With Remainders

Long division with remainders stops at a whole-number quotient and reports the leftover value. The remainder always stays below the divisor. For 9 ÷ 4 = 2 R1, the divisor 4 fits into 9 two times, and 1 is left over. The Long Division Calculator writes a remainder as "R" followed by the leftover value, converts it into a fraction, or continues into the decimal point on request.

An Example of Long Division with Remainders

Divide 100 by 7 to see long division with remainders in full. Set up the problem with 100 inside the division bracket and 7 to the left.

1. 7 fits into 10 one time. Write 1 above the bracket, write 7 below, and subtract: 10 − 7 = 3.
2. Bring down the 0 to form 30.
3. 7 fits into 30 four times. Write 4 above the bracket, write 28 below, and subtract: 30 − 28 = 2.
4. No digits remain, and 2 is smaller than 7.

The quotient is 14 and the remainder is 2, so 100 ÷ 7 = 14 R2. Continuing past the decimal point gives a non-terminating decimal, 14.285714…, or the mixed number 14 2/7.

Example Problems & Step-by-Step Solutions

The Long Division Calculator solves whole-number, decimal, and repeating problems with the same step-by-step layout.

     15 R7
32 ) 487
     32
     --
     167
     160
     ---
       7

156.25
  (terminating decimal)
625 ÷ 4 = 156.25

0.333…
  (repeating decimal)
1 ÷ 3 = 0.3 with overline

Example 1 — Whole-number remainder: 487 ÷ 32

1. 32 fits into 48 one time. Subtract 32 from 48 to get 16.
2. Bring down the 7 to form 167.
3. 32 fits into 167 five times. Subtract 160 from 167 to get 7.
4. The quotient is 15 and the remainder is 7, so 487 ÷ 32 = 15 R7.

Example 2 — Terminating decimal: 625 ÷ 4

1. Divide 625 by 4 to reach 156 with a remainder of 1.
2. Add a decimal point and bring down a 0.
3. Continue the division to reach 156.25, a terminating decimal.

Example 3 — Repeating decimal: 1 ÷ 3

1. 3 does not fit into 1, so the whole-number quotient is 0.
2. Add a decimal point, bring down a 0, and divide 10 by 3 to get 3 with a remainder of 1.
3. The same remainder repeats, so the answer is the repeating decimal 0.333…

Worked Examples

How do you divide 845 by 6 with a remainder?

To divide 845 by 6 with a remainder, run the long division steps to get 845 ÷ 6 = 140 R5. 6 fits into 8 one time, leaving 2; bring down the 4 to form 24, and 6 fits four times with no leftover; bring down the 5, and 6 does not fit, so the quotient digit is 0 and 5 stays as the remainder. Check: 6 × 140 + 5 = 845.

What is 125 ÷ 5?

125 ÷ 5 = 25 with no remainder. 5 fits into 12 two times, leaving 2; bring down the 5 to form 25, and 5 fits five times exactly. Check: 5 × 25 = 125, so the division is even and the remainder is 0.

How do you handle 7 ÷ 16?

To handle 7 ÷ 16, divide the smaller number by the larger number to get the decimal 0.4375. The divisor 16 does not fit into 7, so the whole-number quotient is 0. Add a decimal point, bring down zeros, and continue the division: 7 ÷ 16 = 0.4375, a terminating decimal.

Key Concepts

The Long Division Calculator relies on 8 core concepts:

• Dividend — the number being divided.
• Divisor — the number that divides the dividend.
• Quotient — the result of the division.
• Remainder — the leftover value, always smaller than the divisor.
• Radicand — the region under the division bracket that holds the dividend.
• Terminating decimal — a quotient that ends, such as 156.25.
• Repeating decimal — a quotient with a cycling digit pattern, such as 0.333…
• Non-terminating decimal — a quotient that never ends, such as 14.285714…

An uneven division also produces a mixed number, which pairs the whole-number quotient with the remainder written as a fraction over the divisor, such as 14 2/7.

Applications

Long division supports 6 common applications, including checking arithmetic, dividing money, and finding square roots. Long division checks a calculator answer by hand. Long division splits a bill or a budget across equal shares. Long division finds a square root through the square root long division method. Long division divides algebraic expressions and polynomials. Long division computes checksums in networking through binary division. Long division builds early number sense for students in grades 4 to 6.

Common Mistakes

Long division produces 5 common mistakes:

• Forgetting to bring down the next digit before the next divide step.
• Misaligning digits above the division bracket, which shifts the quotient.
• Skipping a 0 in the quotient when the divisor does not fit the partial dividend.
• Stopping the division before every digit has been brought down.
• Confusing the remainder with the decimal answer instead of choosing one output mode.

The Long Division Calculator prevents these mistakes by aligning each column and marking every bring down digit in the work shown.

Frequently Asked Questions