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

Long division is one of the few arithmetic methods that genuinely shows its own work: every digit of the answer comes from a visible, checkable step, rather than appearing all at once. This guide walks through how to do long division step by step with a complete example digit by digit, verified by hand, and covers both ways a division can end, with a clean remainder, or continued into a decimal that either terminates or repeats forever. For an instant answer with the exact same working shown automatically, the long division calculator computes the quotient, remainder, and full step-by-step table for any two whole numbers, continuing into the decimal places whenever there's a remainder.

How to do long division: the four moves behind every problem

Every step of long division repeats the same four moves in order:

1. Bring down the next digit (or digits) of the dividend to build a partial dividend.
2. Divide: work out how many times the divisor fits into that partial dividend as a whole number.
3. Multiply the divisor by that count.
4. Subtract the result from the partial dividend, and carry whatever is left over into the next step.

That is the entire method. Every worked example below, no matter how many digits are involved, is just this same four-move cycle repeated.

Worked example 1: an exact division, 938 divided by 7

Start with the dividend's digits: 9, 3, 8.

Step 1. The first digit is 9. 7 fits into 9 exactly once (1 x 7 = 7), leaving a remainder of 9 - 7 = 2. First quotient digit: 1.

Step 2. Bring down the next digit, 3, and attach it to the remainder from step 1: 2 becomes 23. 7 fits into 23 exactly three times (3 x 7 = 21), leaving a remainder of 23 - 21 = 2. Next quotient digit: 3.

Step 3. Bring down the last digit, 8, and attach it to the remainder from step 2: 2 becomes 28. 7 fits into 28 exactly four times (4 x 7 = 28), leaving a remainder of 28 - 28 = 0. Next quotient digit: 4.

Reading the quotient digits in order, 1, 3, 4, gives 134, with a final remainder of 0. Checking the answer: 134 x 7 = 938, which matches the original dividend exactly, confirming the division is exact with nothing left over.

Worked example 2: a division with a remainder, 875 divided by 24

Start with the dividend's digits: 8, 7, 5.

Step 1. The first digit alone, 8, is smaller than the divisor, 24, so no quotient digit can be found yet. Bring down the next digit, 7, to form 87. 24 fits into 87 exactly three times (3 x 24 = 72), leaving a remainder of 87 - 72 = 15. First quotient digit: 3.

Step 2. Bring down the last digit, 5, and attach it to the remainder from step 1: 15 becomes 155. 24 fits into 155 exactly six times (6 x 24 = 144), leaving a remainder of 155 - 144 = 11. Next quotient digit: 6.

Reading the quotient digits in order, 3, 6, gives 36, with a final remainder of 11. Checking the answer: 36 x 24 = 864, plus the remainder 11, equals 875, which matches the original dividend exactly.

As a fraction, this result is written 36 and 11/24: the whole-number quotient, plus the remainder over the divisor. Since 11 and 24 share no common factor besides 1, that fraction is already in its simplest form.

Continuing the same division into a decimal

The division above does not have to stop at a remainder. Continuing past the decimal point uses the exact same four-move cycle, just bringing down a 0 (as if the dividend continued 875.000000...) instead of a real digit each time.

Decimal step 1. Carry forward the remainder, 11, and bring down a 0: 110. 24 fits into 110 exactly four times (4 x 24 = 96), leaving a remainder of 110 - 96 = 14. Decimal digit: 4.

Decimal step 2. Bring down another 0, attaching it to 14: 140. 24 fits into 140 exactly five times (5 x 24 = 120), leaving a remainder of 140 - 120 = 20. Decimal digit: 5.

Decimal step 3. Bring down another 0, attaching it to 20: 200. 24 fits into 200 exactly eight times (8 x 24 = 192), leaving a remainder of 200 - 192 = 8. Decimal digit: 8.

Decimal step 4. Bring down another 0, attaching it to 8: 80. 24 fits into 80 exactly three times (3 x 24 = 72), leaving a remainder of 80 - 72 = 8. Decimal digit: 3.

At this point, the remainder is 8 again, the exact same value carried into decimal step 4. Once a remainder repeats a value seen earlier, the digits from that point on are guaranteed to repeat forever too, since the same remainder will keep producing the exact same next digit and the exact same next remainder every time. So 875 divided by 24 is 36.4583, with the final 3 repeating forever: 36.45833333... This is usually written 36.458̄3̄ or with a bar over the repeating part, here just the final 3.

Reading the two forms side by side

All three describe the exact same division; none of them is more "correct" than another, they just suit different purposes. A useful habit is picking the form that matches what the number will be used for next: a recipe scaled down for fewer servings usually reads more naturally as a fraction (36 and 11/24 cups, say), a shared bill split among friends is usually rounded to a decimal (since currency is normally tracked to two decimal places), and a remainder-and-quotient form is often clearest when the leftover amount itself matters, such as packing 875 items into boxes of 24 and needing to know exactly how many items are left over once 36 full boxes are packed.

Quick answers to common division questions

Some division problems come up again and again, and it helps to know the answers without working through the whole bracket each time. The table lists the quotient, the remainder and the decimal for a set of frequent ones. Each row is the same four-move method, so you can use it as a check on your own long division, or as a set of practice problems to work by hand and compare against.

Two patterns stand out. When the divisor is larger than the dividend, as in 18 divided by 20 or 3 divided by 13, the quotient is 0 and the whole dividend is the remainder, so the answer is a pure decimal. And divisors whose only prime factors are 2 and 5 always terminate, which is why 13 divided by 4 ends at 3.25 while 13 divided by 3 never stops.

Not every decimal terminates

The 875 / 24 example above happens to settle into a repeating decimal after four digits, but it's worth knowing in advance which divisions terminate cleanly and which don't, so a repeating pattern doesn't look like a mistake. A division terminates in a finite number of decimal digits only when the divisor's prime factors, once any common factors with the dividend are removed, are made up entirely of 2s and 5s (since our number system is base 10, and 10 = 2 x 5). The divisor 24 factors into 2^3 x 3, and that leftover factor of 3 is exactly why 875 / 24 never terminates and instead repeats forever. By contrast, 17 divided by 5 terminates after a single decimal digit (3.4), because 5 itself is made up only of the prime factor 5, with nothing else left over to cause a repeat.

Worked example 3: a larger dividend, 4,725 divided by 15

Larger numbers follow the exact same four-move cycle; they simply need more repetitions of it. Start with the dividend's digits: 4, 7, 2, 5.

Step 1. The first digit alone, 4, is smaller than the divisor, 15, so no quotient digit can be found yet. Bring down the next digit, 7, to form 47. 15 fits into 47 exactly three times (3 x 15 = 45), leaving a remainder of 47 - 45 = 2. First quotient digit: 3.

Step 2. Bring down the next digit, 2, and attach it to the remainder from step 1: 2 becomes 22. 15 fits into 22 exactly once (1 x 15 = 15), leaving a remainder of 22 - 15 = 7. Next quotient digit: 1.

Step 3. Bring down the last digit, 5, and attach it to the remainder from step 2: 7 becomes 75. 15 fits into 75 exactly five times (5 x 15 = 75), leaving a remainder of 75 - 75 = 0. Next quotient digit: 5.

Reading the quotient digits in order, 3, 1, 5, gives 315, with a final remainder of 0. Checking the answer: 315 x 15 = 4,725, which matches the original dividend exactly, confirming an exact division.

Notice that this larger dividend needed three working steps instead of two, one for each digit brought down after the first digit that was too small on its own, but every single step followed the identical bring-down-divide-multiply-subtract pattern used in the two smaller examples earlier.

Estimating a quotient digit quickly

Finding how many times a two-digit or larger divisor fits into a partial dividend can feel like guesswork without a system. A reliable shortcut is rounding both numbers to their leading digit before dividing, then checking the estimate against the real numbers. For step 1 of the 4,725 / 15 example above, rounding 15 to 20 (its nearest "friendly" ten) and 47 to roughly 47, estimate 47 / 20, which is a little more than 2, suggesting the real answer is 2 or 3. Testing 3: 3 x 15 = 45, which fits under 47 with a small remainder left; testing 4: 4 x 15 = 60, which is too large. So 3 is confirmed as the correct quotient digit, reached with one estimate and one or two quick checks rather than trial and error from 1 upward.

This estimating habit becomes increasingly valuable as the divisor gets larger; for a two-digit or three-digit divisor, checking every possible digit from 1 to 9 by full multiplication is slow, while a rounded estimate usually narrows the search down to one or two candidates immediately.

Why long division is still worth learning by hand

A calculator produces a quotient and remainder instantly, so it's fair to ask why learning how to do long division by hand still matters. Three reasons hold up well. First, standardized tests and many classroom settings specifically restrict calculators for this exact skill, making it a practical necessity rather than a nostalgic exercise. Second, the same digit-by-digit logic used here underlies converting any fraction to a decimal, a skill that comes up constantly in measurement, cooking, finance, and science. Third, understanding the mechanical process behind division builds real number sense: someone who has done long division by hand can sanity-check whether a calculator's answer is even in the right ballpark, catching a misplaced decimal point or a mistyped number before it quietly derails a larger calculation.

Common mistakes to watch for

Misaligning digits, especially when a quotient needs a 0 in the middle. Dividing 408 by 4, for instance, produces a 0 in the tens place of the quotient, because after the first quotient digit is found, the next partial dividend is too small for 4 to fit even once, before another digit is brought down. Skipping that 0 rather than writing it down shifts every digit after it out of place, producing a quotient with the right digits but the wrong value entirely.

Forgetting to bring down a digit, which usually shows up as a quotient with too few digits compared to the size of the dividend, since each digit of the original dividend should correspond to exactly one step of the working (skipping past the first one or two digits that don't yet reach the divisor).

Subtracting incorrectly at any single step, which carries a wrong remainder into every step that follows, even when every other part of the method is applied correctly. This is exactly why the multiplication check below is worth doing every time, not just when an answer looks suspicious.

What to do when the divisor itself is a decimal

Every worked example above uses a whole-number divisor, but long division still works when the divisor has a decimal point, once one extra move is added at the start: multiply both the dividend and the divisor by the same power of 10, chosen to turn the divisor into a whole number. This does not change the answer, since multiplying both numbers in a division by the same amount is the same as multiplying by 1 (10 divided by 10), so the quotient comes out identical either way.

Worked example: 12.5 divided by 0.25. The divisor, 0.25, has two decimal places, so multiply both numbers by 100: 12.5 becomes 1250, and 0.25 becomes 25. The problem is now 1250 divided by 25, a whole-number division that uses the exact same four-move cycle as every example earlier in this guide. The first two digits, 12, are too small for 25 to fit into, so bring down the third digit to form 125; 25 fits into 125 exactly five times (5 x 25 = 125), leaving no remainder. Bring down the final digit, 0, forming 0; 25 fits into 0 exactly zero times. Reading the quotient digits in order, 5 then 0, gives 50.

Checking the answer against the original problem: 0.25 x 50 = 12.5, which matches the original dividend exactly, confirming that 12.5 divided by 0.25 really is 50.

This is exactly why this site's long division calculator restricts its inputs to whole numbers: the digit-by-digit working shown on the page matches the pencil-and-paper method precisely only once any decimal point in the divisor has already been shifted away this same way. Doing that shift by hand first, then typing in the resulting whole-number dividend and divisor, gets the identical step-by-step working for a decimal division problem that the tool would otherwise not accept directly.

Check your answer

Multiply the quotient by the divisor, then add the remainder; the result should equal the original dividend exactly. For 875 divided by 24: 36 x 24 = 864, plus the remainder 11, equals 875, confirming the whole-number result. For the decimal form, multiplying 36.45833... by 24 should land back on 875 as well (allowing for the repeating decimal being cut off after a few digits). This single check, one multiplication and one addition, catches misaligned digits, skipped steps, and subtraction mistakes all at once. That covers how to do long division by hand from start to finish; for an instant version of the same full working, remainder, fraction, and continued decimal, shown automatically, the long division calculator computes all of it for any dividend and divisor you enter.