How to Do Long Division
Divide by one- and two-digit numbers on paper with worked examples, three ways to write a remainder, zeros in the quotient, and a check by multiplying back.
You will end up able to divide a whole number by a one- or two-digit divisor on paper, write what is left over as a remainder, a fraction, or a decimal, and prove the answer is right by multiplying back.
The method is four moves repeated in a loop: divide, multiply, subtract, and bring down the next digit. Every step below works through real numbers, so copy them onto paper and follow along. No calculator is needed.
Pencil Paper Eraser
Set up the problem
Write the dividend (the number being divided) under the long division bracket. Write the divisor (the number you are dividing by) to the left, outside the bracket. Leave space above the bracket for the quotient, which is the answer you are building digit by digit. For 845 ÷ 3, the 845 goes inside the bracket and the 3 goes outside. If anything is left over at the end, that is the remainder.
Good to know: Long division starts from the leftmost digit of the dividend, the opposite end from addition and subtraction. FAQ 4 below explains why.
Divide the first digit
Look at the leftmost digit of the dividend and ask how many times the divisor fits into it. With 845 ÷ 3, look at the 8. How many times does 3 fit into 8? Twice, because 3 × 2 = 6, and 3 × 3 = 9 would be too large. Write the 2 above the 8 in the quotient. If the divisor is larger than the first digit, include the next digit as well, and keep adding digits until the number is at least as large as the divisor. Write the first quotient digit above the last digit you included. For 245 ÷ 38, the 38 does not fit into 2 or into 24, so take all three digits. 38 × 6 = 228 and 38 × 7 = 266, which is too large, so write 6 above the 5.
Multiply and subtract
Multiply the quotient digit you just wrote by the divisor and write the result below the working number. Then subtract. You wrote 2 above, and the divisor is 3. So 3 × 2 = 6. Write the 6 below the 8. Now subtract: 8 − 6 = 2. If the product is larger than the number above it, you cannot subtract, and the quotient digit is too big. Lower it by one and multiply again. The difference must be smaller than the divisor. If it is equal to or larger than the divisor, the quotient digit was too small. Raise it by one and check again.
Heads up: Check every subtraction before you bring the next digit down. Add the difference to the number you subtracted, and you should get the number above them. Here 2 + 6 = 8, so the subtraction is right.
Bring down the next digit
Take the next digit of the dividend and bring it down next to the difference from the previous subtraction. This forms a new working number. The difference was 2, and the next digit in 845 is 4. Bring the 4 down to make 24. Now repeat the cycle: divide 24 by 3. That gives 8, because 3 × 8 = 24. Write 8 above the 4 in the quotient. Multiply: 3 × 8 = 24. Subtract: 24 − 24 = 0.
Repeat until there are no digits left
Bring down the next digit. The 5 comes down, making the working number 5. (A leading zero after subtraction just means 05, which is 5.) Divide: 3 goes into 5 once, because 3 × 1 = 3. Write 1 above the 5. Multiply: 3 × 1 = 3. Subtract: 5 − 3 = 2. There are no more digits to bring down, so the division is done. The quotient is 281 and the remainder is 2. 845 ÷ 3 = 281 remainder 2.
Handle the remainder
You can express a remainder in three different ways, depending on what you need. As a whole-number remainder: 845 ÷ 3 = 281 R 2. Use this when the leftover cannot be split, such as 845 marbles shared among 3 people, where each person gets 281 and 2 are left over. As a fraction: Put the remainder over the divisor. 845 ÷ 3 = 281 2/3. As a decimal: Instead of stopping, write a decimal point and a zero after the dividend, and put a decimal point in the quotient directly above it. Bring the zero down and keep dividing. 3 goes into 20 six times (3 × 6 = 18), leaving 2 again. This repeats forever, giving 281.666..., written as 281.6 with a bar over the 6. Round to the place you need, such as 281.67 to two decimal places for money. If the remainder is 0, the division is exact and there is nothing left to express.
Tackle a two-digit divisor
The steps are identical, but you look at more digits at a time. Try 1,260 ÷ 24. 24 does not fit into 1, and it does not fit into 12 either, because 12 is less than 24. So take the first three digits, 126. 24 × 5 = 120, and 24 × 6 = 144 is too large. Write 5 in the quotient above the 6. Subtract: 126 − 120 = 6. Bring down the 0, making 60. 24 × 2 = 48. Write 2 above the 0. Subtract: 60 − 48 = 12. There are no more digits to bring down. 1,260 ÷ 24 = 52 remainder 12.
Good to know: Before you start dividing by a two-digit number, write out the first nine multiples of the divisor on the side of your paper (24, 48, 72, 96, 120, 144, 168, 192, 216). This turns the guessing step into a simple lookup.
Watch out for zeros in the quotient
When you bring down a digit and the divisor does not fit into the new working number, you must write a 0 in the quotient and bring down the next digit. Example: 832 ÷ 8 8 ÷ 8 = 1. Write 1. Subtract: 8 − 8 = 0. Bring down the 3. 8 does not fit into 3. Write 0 in the quotient. Bring down the 2, making 32. 8 × 4 = 32. Write 4. Subtract: 32 − 32 = 0. Answer: 104. If you skip the zero, you get 14, and the check in step 9 catches it, because 14 × 8 = 112, not 832. Every time you bring down a digit, exactly one digit must be written in the quotient, even if that digit is 0.
Check your answer
Multiply the quotient by the divisor and add the remainder. The result should equal the original dividend. 845 ÷ 3 = 281 R 2 Check: 281 × 3 = 843. Then 843 + 2 = 845. Correct. 1,260 ÷ 24 = 52 R 12 Check: 52 × 24 = 1,248. Then 1,248 + 12 = 1,260. Correct. Then confirm one more thing, that the remainder is smaller than the divisor. Without that, a quotient that is too small can slip through, because 280 × 3 + 5 also makes 845. When both checks pass, the answer is right, because only one quotient and remainder satisfy both. Run them on every problem.
Practice with single-digit divisors until you can run the loop without looking back at the steps, then move to two-digit divisors with the multiples list from step 7. Rework the examples above with the answers covered, then check yours against them. If a check in step 9 fails, count the digits in your quotient. After the first quotient digit, every digit you bring down adds exactly one more, so 845 ÷ 3 needs three digits and 1,260 ÷ 24 needs two. A quotient with too few digits is missing a 0 (step 8). If the digit count is right, redo the subtraction check from step 3 line by line, and the first line where it fails is the mistake. For divisors with a decimal point, see FAQ 2 below.
Questions we get asked about this
Answers from experience, not a textbook.
Use the mnemonic "Does McDonald's Sell Burgers?" for Divide, Multiply, Subtract, Bring down. Repeat these four steps in a cycle until there are no more digits to bring down. The check from step 9 comes after the last cycle.
Yes. If the divisor has a decimal, move the decimal point to the right until it becomes a whole number, then move the dividend's decimal point the same number of places. Place the decimal point in the quotient directly above its position in the dividend and proceed with the normal steps. For 7.5 ÷ 0.25, move both decimal points two places to the right, adding a zero to the dividend, which gives 750 ÷ 25 = 30.
Short division is a compact version used when the divisor is a single digit. The multiply-and-subtract steps are done in your head, and only the carried remainders are noted. Long division writes every step out, which makes it easier to follow when the divisor has two or more digits.
Because you are figuring out the largest place value first. Starting from the leftmost digit lets you determine how many hundreds, then tens, then ones the divisor fits into. Addition and subtraction start from the right because what carries or borrows moves from a smaller place to a larger one. In division, what is left over moves the other way. In 845 ÷ 3, the 2 hundreds left over after the first step become 20 tens, which join the 4 tens to make 24.
Cover the last digit of the divisor and the last digit of the working number, then divide what is left and keep the whole-number part. For 126 ÷ 24 in step 7, that is 12 ÷ 2 = 6. Multiply to test it. 24 × 6 = 144, which is larger than 126, so lower the guess to 5. 24 × 5 = 120 fits, and 126 − 120 = 6 is smaller than 24, so 5 is right. This guess is never too small, only exact or too big, so you only ever count down from it. If it comes out above 9, start at 9.