How to Do Long Division: Step-by-Step Guide

How to Do Long Division

Do long division by repeating five steps in order: divide, multiply, subtract, bring down, and repeat. Divide the leftmost part of the dividend by the divisor, multiply the quotient digit by the divisor, subtract the product, then bring down the next digit. Continue the sequence until every digit has been used, and the final leftover value becomes the remainder.

Long division breaks one large division problem into a short sequence you repeat digit by digit. The Long Division Calculator runs the sequence and prints each step, but the method below shows the reasoning so any answer can be checked and understood by hand.

The Parts of a Long Division Problem

A long division problem has 4 parts, each with a fixed position:

1. Dividend, the number being divided, written inside the division bracket.
2. Divisor, the number you divide by, written to the left of the bracket.
3. Quotient, the answer, written above the bracket.
4. Remainder, the leftover value, always smaller than the divisor.

For the division 487 ÷ 32 = 15 R7, the dividend is 487, the divisor is 32, the quotient is 15, and the remainder is 7. These four values connect through one identity, covered in the checking section below.

The Five Steps of Long Division

Long division repeats the same five steps until no digits remain. Each pass produces one digit of the quotient.

1. Divide the smallest part of the dividend the divisor fits into, and write the result above the bracket.
2. Multiply the new quotient digit by the divisor, and write the product below the partial dividend.
3. Subtract the product from the partial dividend to find the leftover value.
4. Bring down the next digit of the dividend, and place it beside the leftover value.
5. Repeat the divide, multiply, and subtract steps until every digit has been brought down.

The leftover value after each subtraction always stays smaller than the divisor. When no digits remain, the last leftover value is the remainder. The Long Division Calculator with Steps shows the bracket setup, each subtraction, and every digit brought down.

Worked Example: 100 Divided by 7

Divide 100 by 7 to see the five steps in full. Write 100 inside the bracket and 7 to the left.

1. Divide: 7 fits into 10 one time. Write 1 above the bracket.
2. Multiply: 1 × 7 = 7. Write 7 below the 10.
3. Subtract: 10 − 7 = 3.
4. Bring down: bring down the 0 to form 30.
5. Repeat: 7 fits into 30 four times. Write 4 above the bracket, write 28 below, and subtract: 30 − 28 = 2.

No digits remain, and 2 is smaller than 7, so the quotient is 14 and the remainder is 2. The answer is 100 ÷ 7 = 14 R2. Continuing past a decimal point gives the non-terminating decimal 14.285714….

How to Do 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, because a leftover equal to or larger than the divisor means the last quotient digit was too small.

For 9 ÷ 4, the divisor 4 fits into 9 two times, and 1 is left over, so the answer is 2 R1. For 845 ÷ 6, the divisor 6 fits into 8 once, into 24 four times, and does not fit into the final 5, so the quotient gains a 0 and the answer is 140 R5. Writing the 0 in the quotient holds the place value and keeps the digits aligned. The Long Division Calculator with Remainders reports the quotient and the leftover value for any pair.

How to Do Long Division With Decimals

Long division continues past the decimal point when an exact value is needed. After the whole-number quotient, add a decimal point, bring down a zero, and keep dividing. For 625 ÷ 4, the whole-number result is 156 with a remainder of 1; adding a decimal point and continuing gives 156.25, a terminating decimal.

A repeating remainder produces a repeating decimal. For 1 ÷ 3, the divisor never divides evenly, the same remainder returns, and the answer is 0.333…. When a divisor has a decimal, multiply both the dividend and the divisor by the same power of 10 first, which leaves the quotient unchanged and keeps the workspace in whole numbers. The Long Division Calculator with Decimals marks repeating digits and places the decimal point in the quotient.

How to Check a Long Division Answer

Check a long division answer with the identity Dividend = Divisor × Quotient + Remainder. Every division problem satisfies this identity, so it confirms any result. For 487 ÷ 32 = 15 R7, multiply 32 by 15 to get 480, then add the remainder 7 to reach 487, which matches the dividend.

The remainder rule completes the check: the remainder must be 0 or greater and smaller than the divisor. A remainder equal to or larger than the divisor signals that a quotient digit was too small, and a negative leftover signals a subtraction error. Reworking the step fixes the answer.

Common Mistakes in Long Division

Three common mistakes appear in long division:

1. Forgetting to bring down the next digit before the next divide step.
2. Skipping a 0 in the quotient when the divisor does not fit the partial dividend, which shifts every later digit.
3. Misaligning the quotient digits above the bracket, which changes their place value.

Two further errors distort the result. Stopping before every digit has been brought down leaves the division unfinished, so continue until no digits remain or decimal mode is chosen. Reporting both a remainder and a decimal for the same problem mixes two output forms, so pick one. The Long Division Calculator aligns each column and marks every digit brought down to prevent these errors.

Frequently Asked Questions

How do you do long division step by step?

Repeat five steps in order: divide, multiply, subtract, bring down, and repeat. Divide the partial dividend by the divisor, multiply the quotient digit by the divisor, subtract the product, then bring down the next digit. Continue until no digits remain, and the final leftover value is the remainder.

What are the parts of a long division problem?

A long division problem has four parts: the dividend, the divisor, the quotient, and the remainder. The dividend is the number being divided, the divisor is the number you divide by, the quotient is the answer, and the remainder is the leftover value, which is always smaller than the divisor.

How do you check a long division answer?

Check a long division answer with the identity Dividend equals Divisor times Quotient plus Remainder. For 487 divided by 32 equals 15 remainder 7, multiply 32 by 15 to get 480, then add 7 to reach 487, which matches the dividend and confirms the answer.

How do you do long division with a remainder?

Stop the division at a whole-number quotient and report the leftover value as the remainder. The remainder is always smaller than the divisor. For 9 divided by 4, the divisor 4 fits into 9 two times with 1 left over, so the answer is 2 remainder 1.

Can you divide a smaller number by a larger number with long division?

Yes. When the dividend is smaller than the divisor, the whole-number quotient is 0. Add a decimal point and bring down zeros to continue in decimal mode. For 7 divided by 16, the divisor does not fit into 7, and the decimal answer is 0.4375.