Long division is the algorithm people forget first and dread most, usually because it was taught as a sequence of moves with no explanation of what any of them meant. It is actually one idea repeated: how many of these fit into that, take them away, bring down the next digit, repeat. This walks through it with the reasoning attached, compares it with chunking, and deals with the two things that cause most of the trouble — remainders and decimals.
There are two questions hiding under the same symbol, and knowing which one you are answering makes the arithmetic easier.
Sharing: 84 ÷ 4 as 'split 84 into 4 equal groups — how big is each?' This is the version that fits money and portions.
Grouping: 84 ÷ 4 as 'how many 4s fit into 84?' This is the version the long division algorithm actually performs, and it is why the method works by repeatedly asking 'how many fit'.
Both give 21, and they always will. But for a question like 'how many buses do I need for 84 people at 50 each', the grouping version is the one that makes the remainder mean something.
Take 912 ÷ 4. Written in the bus stop layout, you work left to right through the digits of 912.
How many 4s in 9? Two, with 1 left over. Write 2 above the 9 and carry the 1.
The carried 1 joins the next digit, making 11. How many 4s in 11? Two, with 3 left over. Write 2 above the 1 and carry the 3.
The carried 3 joins the last digit, making 32. How many 4s in 32? Exactly 8. Write 8 above the 2.
Read the answer off the top: 228.
Check it by multiplying back: 228 × 4 = 912. That check costs one multiplication and catches almost every slip, which makes skipping it a false economy.
Every step is a times-table fact plus a subtraction. That is why division feels hard when the tables are slow — the algorithm is fine, but each step is being recalculated. Missing Factor drills exactly the retrieval this needs.
With a two-digit divisor there is no single-digit fact to reach for, so the working is written out underneath instead of carried. Take 1,014 ÷ 26.
How many 26s in 101? Estimate: 26 is close to 25, and four 25s are 100, so try 3. 26 × 3 = 78. Write 3 above, write 78 underneath, subtract: 101 − 78 = 23.
Bring down the next digit, making 234.
How many 26s in 234? 26 × 9 = 234 exactly. Write 9 above, subtract to leave 0.
The answer is 39, with no remainder. Check: 39 × 26 = 1,014.
The estimate in step one is the part worth practising. Rounding the divisor to something friendly — 26 to 25, 19 to 20, 31 to 30 — turns each step into a quick guess you then correct, rather than a search.
Chunking subtracts easy multiples instead of finding the exact digit each time. For 1014 ÷ 26: take away 26 × 30 = 780, leaving 234. Take away 26 × 9 = 234, leaving 0. Add the chunks: 30 + 9 = 39.
It takes more lines and it is far harder to get badly wrong, because every step is a multiplication you actually know rather than an estimate you have to nail. For anyone who finds long division fragile, this is the method that works.
It also scales down neatly to mental division. 1014 ÷ 26 in your head is 'thirty of them is 780, that leaves 234, that is nine more, so 39' — which is chunking without the paper.
Leaving a remainder
85 ÷ 4 is 21 remainder 1. That is the right answer when the thing being divided cannot be split — people, buses, boxes. It is the wrong answer for a measurement.
Carrying on into decimals
To continue, put a decimal point after the 21 and add a zero to the remainder: 10 ÷ 4 = 2 with 2 left, then 20 ÷ 4 = 5 exactly. So 85 ÷ 4 = 21.25. Nothing new is happening — the same 'how many fit' question, one place value further right.
When it never ends
1 ÷ 3 gives 0.333… and never stops, because 3 does not divide into any power of ten. A division terminates only when the divisor, once the fraction is in lowest terms, is built from 2s and 5s. Anything else repeats, and it repeats in a pattern.
Rounding the answer
Take the division one place further than you need, then round. Stopping at the place you want and rounding what you have there is how answers end up one out.
Losing a place value. A zero in the middle of an answer gets dropped, so 2,040 ÷ 4 comes out as 51 instead of 510. Counting the digits of the answer before starting prevents it.
Forgetting to bring a digit down. Everything after that point is wrong. Ticking each digit as it comes down is a cheap fix.
Guessing the digit too high. The subtraction then goes negative, which is the signal to reduce the guess by one and try again — not to carry on.
Slow times tables. Every step is a table fact. If those take two seconds each, the whole division takes a minute and the working memory needed to track the place values has already gone.
That last one is the real cause most of the time. If long division feels impossible, the fix is usually not more long division — it is getting the tables to instant recall first.
Ask how many times the divisor fits into the leading part of the number, write that digit above, multiply back and subtract, bring down the next digit, and repeat until no digits remain.
The short division layout, where the number sits under a bracket and remainders are carried across to the next digit rather than written out underneath. It works when the divisor is a single digit.
Repeatedly subtracting easy multiples of the divisor and adding up how many you took. For 1014 ÷ 26, take away thirty 26s (780) then nine more (234), giving 39.
Put a decimal point in the answer, add a zero to the remainder, and carry on dividing. 85 ÷ 4 is 21 remainder 1, and continuing gives 21.25.
Because the divisor has a prime factor other than 2 or 5. 1 ÷ 3 repeats forever; 1 ÷ 8 terminates at 0.125.
Multiply the answer by the divisor and add any remainder. It should give back exactly the number you started with.
Long division is one question asked repeatedly, and it collapses the moment the times tables are instant. Check yours on the [Times Table Check](/tools/times-table-check), drill the backwards direction on [Missing Factor](/games/missing-factor), and see the multiplication laid out on [Long Multiplication](/tools/long-multiplication).