Long Division Calculator

What Is Long Division?

Long division is a method for dividing large numbers by breaking the calculation into a sequence of smaller steps. Unlike short division, which is done mentally or in one line, long division writes out each step explicitly — making it easy to follow and verify. The method works by dividing the dividend digit by digit from left to right, computing a quotient digit at each position, multiplying back to find the product, subtracting to find the new remainder, and bringing down the next digit.

Long division is the standard algorithm taught in schools for integer division. It produces both a whole-number quotient and a remainder, and can be extended into the decimal places by treating the remainder as a decimal dividend and continuing the process. The calculator above shows all steps so you can check homework, verify calculations, or learn the method.

Long Division Terms

Understanding the vocabulary of division is essential before working through the steps. Each term has a specific role in the calculation.

Dividend

The dividend is the number being divided. It is the larger number (in most cases) that you want to split into equal groups. In the expression 845 ÷ 7, the dividend is 845. In the traditional long division bracket notation, the dividend is written inside the bracket on the right.

Divisor

The divisor is the number you are dividing by. It represents the size of each group or the number of groups you are splitting the dividend into. In 845 ÷ 7, the divisor is 7. In the bracket notation, the divisor is written outside and to the left of the bracket. A divisor of zero is undefined and cannot be used.

Quotient

The quotient is the result of the division — the whole number answer. When 845 is divided by 7, the quotient is 120 (with a remainder of 5). The quotient is written above the dividend in the traditional bracket format and can be verified by multiplying it back by the divisor and adding the remainder.

Remainder

The remainder is the amount left over after the divisor has been subtracted as many times as possible. It is always less than the divisor. When 845 ÷ 7 = 120 remainder 5, the remainder 5 is less than 7, confirming the division is complete. A remainder of zero means the dividend is perfectly divisible by the divisor. The remainder can also be expressed as a fraction (remainder/divisor) or continued as a decimal.

How to Do Long Division Step by Step

Long division follows a repeating four-step cycle: Divide, Multiply, Subtract, Bring Down. These four operations are performed for each digit position in the quotient. The example below shows 845 ÷ 7.

Step 1 — Divide

Start with the leftmost digit (or digits) of the dividend that are large enough for the divisor to go into at least once. For 845 ÷ 7, start with 8. Ask: how many times does 7 go into 8? The answer is 1 (because 1 × 7 = 7 and 2 × 7 = 14, which is too large). Write 1 as the first digit of the quotient above the dividend.

Step 2 — Multiply

Multiply the quotient digit you just wrote by the divisor. For this step: 1 × 7 = 7. Write this product below the portion of the dividend you are working with. This product represents the largest multiple of the divisor that fits into the current working number.

Step 3 — Subtract

Subtract the product from the current working number. For this step: 8 − 7 = 1. Write the result below the subtraction line. This result must always be less than the divisor; if it is equal to or larger than the divisor, the quotient digit was too small and needs to be increased by one.

Step 4 — Bring Down

Bring down the next digit of the dividend and append it to the current remainder. After 8 − 7 = 1, bring down the next digit 4 to get 14. This becomes the new working number for the next round of the cycle.

Step 5 — Repeat

Repeat the Divide, Multiply, Subtract, Bring Down cycle with the new working number. For 14 ÷ 7 = 2, write 2 as the next quotient digit. Then 2 × 7 = 14, and 14 − 14 = 0. Bring down the final digit 5, giving working number 5. Since 7 does not go into 5 even once, write 0 as the final quotient digit. The final remainder is 5. The complete quotient is 120, remainder 5.

Long Division Examples

Example — 845 ÷ 7

Example — 1234 ÷ 56

Example — Division with Remainder

Not every division produces a whole number. When 500 is divided by 3, the process continues indefinitely because 3 does not divide evenly into 500. The quotient is 166, and the remainder is 2. Expressed as a decimal, 500 ÷ 3 = 166.666... (the digit 6 repeats forever). This type of result is called a repeating decimal. The calculator shows up to 10 decimal places and indicates when the decimal is repeating.

Long Division with Decimals

When there is a remainder after using all digits of the dividend, the division can be extended into decimal places. To do this, place a decimal point after the quotient and after the dividend, then append a zero to the remainder and continue the long division process. Each zero appended produces one more decimal digit in the quotient.

For example, 17 ÷ 4 = 4 remainder 1. Appending a zero gives 10 ÷ 4 = 2 remainder 2. Appending another zero gives 20 ÷ 4 = 5 remainder 0. The decimal result is 4.25 exactly. When the remainder repeats (the same value appears twice), the decimal repeats forever. The calculator detects repeating decimals and marks them with ellipsis.

For calculations involving more complex arithmetic, the free AI math solver can walk through any arithmetic problem in detail. For percentage-based division problems, the percentage calculator handles those directly.

Checking Your Answer

Division answers should always be verified before accepting them as correct. There are two common checking methods.

Multiply Back Method

The most reliable check is to reverse the operation: multiply the quotient by the divisor, then add the remainder. The result must equal the original dividend exactly.

The calculator automatically performs this verification and displays the check at the bottom of every result. This works for any integer division regardless of the size of the numbers involved.

Frequently Asked Questions