How to Do Long Division
Learn how to do long division step by step with clear examples. Covers single-digit and two-digit divisors, remainders, zeros in the quotient, and how to check your answer.
Long division is one of those skills that seemed impossible in fourth grade, made sense for about a week, and then slowly drifted out of memory. We had to relearn it an embarrassing number of times before it finally stuck. Divide something, multiply something, subtract, bring something down. But in what order? And what happens when the number does not divide evenly?
The entire process is four steps repeated in a loop. Once you see the pattern, it clicks fast. We will walk through it with real numbers so you can follow along on paper.
No calculator required. Just a pencil, some scratch space, and about five minutes.
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. Two terms worth knowing: the dividend is the number being split up, and the divisor is the number doing the splitting. The answer on top is the quotient. If anything is left over at the end, that is the remainder.
Good to know: Unlike addition and subtraction where you start from the right, long division always starts from the leftmost digit of the dividend. Worth fixing in your head before you begin, because the habit runs the other way.
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, take the first two digits together instead. For example, if you were dividing 245 by 38, the divisor does not fit into 2, so you would look at 24 instead. Still too small (24 is less than 38), so you take all three digits and divide 245 by 38.
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. This difference must always be smaller than the divisor. If it is equal to or larger than the divisor, the quotient digit was too small. Go back and increase it by one.
Heads up: Subtraction errors are one of the two classic ways this goes wrong. Take your time here, especially when borrowing is involved.
Bring down the next digit
Take the next digit of the dividend and bring it down next to the remainder from the previous subtraction. This forms a new working number. The remainder 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. This is the standard form in school math. As a fraction: Put the remainder over the divisor. 845 ÷ 3 = 281 2/3. As a decimal: Instead of stopping, add a decimal point and a zero after the dividend. Continue dividing. 3 goes into 20 six times (3 × 6 = 18), leaving 2 again. This repeats, giving 281.666... (or 281.6 repeating). 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 1260 ÷ 24. 24 does not fit into 1. Does not fit into 12 either (12 is less than 24). So take three digits: 126. 24 × 5 = 120. Write 5 in the quotient. Subtract: 126 − 120 = 6. Bring down the 0, making 60. 24 × 2 = 48. Write 2 in the quotient. Subtract: 60 − 48 = 12. No more digits. 1260 ÷ 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
This is the second of those two classic mistakes. 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, which is wildly wrong. 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. 1260 ÷ 24 = 52 R 12 Check: 52 × 24 = 1,248. Then 1,248 + 12 = 1,260. Correct. This takes about ten seconds and catches every kind of error. Make it a habit to check every time.
The whole process comes down to four steps on repeat: divide, multiply, subtract, bring down. Once that loop clicks, the rest is just practice. We recommend starting with single-digit divisors until the rhythm feels automatic, then moving to two-digit ones. The two biggest traps are forgetting the zero in the quotient and making subtraction errors when borrowing. We have made both of those mistakes more times than we would like to admit. If you check every answer by multiplying back, you will catch both before they become a problem.
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. Some people add a fifth letter for Repeat or Remainder.
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.
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 they need to handle carrying and borrowing from smaller to larger places, but division works in the opposite direction.
That means the quotient digit you wrote is too small. Go back and increase it by one, then redo the multiply-and-subtract step. The remainder must always be less than the divisor. If it is not, the division for that step is incomplete.