Ross MackellUK-qualified primary teacher · 10 min read

Your child brings home a Year 6 worksheet. The first question is 672 ÷ 16. They stare at it. You stare at it. Somebody mutters "Does McDonald's Sell Burgers?" and nobody is quite sure why.

Long division has a reputation as the hardest written method in primary school. It isn't, really. It is just four small steps repeated in a loop, and every one of those steps is something your child has already learned. The trouble is that if any one of them is shaky, the whole thing falls apart.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll show you long division step by step, exactly the way UK schools teach it, with worked examples, the trick that makes it far less scary, how to handle remainders, and the three mistakes I see most often.

What is long division?

Long division is the formal written method children use to divide a number with up to four digits by a two-digit number. It appears in the Year 6 national curriculum and comes up in the SATs arithmetic paper every year.

It works exactly like short division (the bus stop method). You still work from left to right, one digit at a time. The only difference is what happens to the leftover amount:

• In short division, you do the subtraction in your head and write the remainder as a tiny number next to the next digit.
• In long division, you write the subtraction out underneath, then bring the next digit down to join the leftover.

That is the whole point of long division. Dividing by 16 is hard to do in your head, so we write everything down where we can see it. Children who find it hard usually aren't confused by the idea. They're running out of working memory, and writing it down fixes that.

What your child needs first

Long division uses four skills at once. If your child is getting stuck, the problem is very often one of these, not long division itself:

• Times tables. Every step starts with "how many 16s fit into 67?" A child who has to count up in 16s from scratch will lose track. My guide on how to learn times tables fast is the place to start.
• Column subtraction. Each step ends with a subtraction, often with exchanging. If that's wobbly, have a look at column addition and subtraction.
• Place value. Knowing that "16 into 67" really means 67 tens, and that the answer digit goes above the 7, is all place value. Here's my guide to what place value is.
• Short division. Children should be confident dividing by a single digit with the bus stop method before they try a two-digit divisor.

This is why I always say arithmetic comes before reasoning. Long division comes at the end of the written methods, and it sits on top of all the others.

The trick: write the multiples first

Here's the single most helpful thing you can teach your child. Before they start, they write out the multiples of the number they're dividing by. No times tables needed beyond adding on.

For 672 ÷ 16, they just keep adding 16:

Now every "how many 16s?" question is just a matter of looking at the list. A quick check: 5 × 16 should be half of 10 × 16. Half of 160 is 80. If those match, the list is right.

Some teachers call this a "ladder" or "multiples list". It takes a minute to write, and it removes almost all of the guessing that makes long division feel so slow.

Long division step by step: 672 ÷ 16

Every step follows the same loop. Children often remember it as D, M, S, B: Divide, Multiply, Subtract, Bring down. (That's where "Does McDonald's Sell Burgers?" comes from.)

Step 1: Divide

How many 16s go into 6? None. So we look at the first two digits instead: how many 16s go into 67? Check the list: 4 × 16 = 64, and 5 × 16 = 80 is too big. So the answer is 4. Write the 4 above the 7.

Step 2: Multiply

4 × 16 = 64. Write 64 underneath the 67.

Step 3: Subtract

67 − 64 = 3. This is the leftover. A quick check: the leftover must always be smaller than 16. If it isn't, you could have fitted another 16 in.

Step 4: Bring down

Bring the next digit, the 2, down next to the 3. Now you have 32.

Repeat the loop

Divide: how many 16s in 32? 2. Write it above the 2. Multiply: 2 × 16 = 32. Subtract: 32 − 32 = 0. There's nothing left to bring down, so you're finished.

672 ÷ 16 = 42. Check it the other way: 42 × 16 = 672. Teaching your child to check with multiplication is one of the best habits you can build, and it uses long multiplication.

A bigger one: 7,335 ÷ 15

Once your child has the loop, bigger numbers just mean more loops. Here's a four-digit number, which is the size they'll see in Year 6 and the SATs.

1. 15 into 7? Doesn't go. Use 73 instead. 4 × 15 = 60. Write 4 above the 3. 73 − 60 = 13.
2. Bring down the 3 to make 133. 8 × 15 = 120 (9 × 15 = 135 is too big). Write 8. 133 − 120 = 13.
3. Bring down the 5 to make 135. 9 × 15 = 135. Write 9. 135 − 135 = 0.

7,335 ÷ 15 = 489. Notice that the steps are exactly the same as the smaller example. Long division never gets harder, it just gets longer.

Long division with remainders

Not every division comes out exactly. Let's try 1,000 ÷ 24.

• 24 into 1? No. 24 into 10? No. 24 into 100: 4 × 24 = 96. Write 4. 100 − 96 = 4.
• Bring down the 0 to make 40. 1 × 24 = 24. Write 1. 40 − 24 = 16.
• There are no more digits to bring down, so 16 is the remainder.

In Year 6, children are expected to write that remainder in three different ways, depending on the question:

The fraction version trips lots of children up, so it's worth practising. The rule is simple: remainder over divisor. 16 left over, dividing by 24, gives ¹⁶⁄₂₄, which simplifies to ²⁄₃.

In word problems, the remainder needs common sense too. If 1,000 children need coaches that seat 24, the answer is 42 coaches, not 41 r 16, because you can't leave 16 children behind. Asking "what does the remainder mean here?" is a great question to get into the habit of.

Long division or short division?

Here's something many parents don't realise: children are allowed to use short division for two-digit divisors, and the national curriculum says so. If your child knows their multiples of 12, 15 or 25 well, the bus stop method is often quicker.

My advice: let your child use whichever they get right. In the Year 6 SATs arithmetic paper, long division questions are worth 2 marks. If the answer is wrong but a formal method is shown with only one small slip, they can often still pick up 1 mark. So whichever method they use, the working must be written down.

You may also see chunking, where children subtract big "chunks" like 10 × 16 at a time. Some schools use it as a stepping stone. It works, but it's slower and it isn't a formal method, so by Year 6 most children are moved on to short or long division.

3 long division mistakes and how to fix them

Mistake 1: Missing a zero in the answer

Try 6,324 ÷ 31. 31 into 63 is 2, leaving 1. Bring down the 2 to make 12. 31 into 12? It doesn't go. This is where children skip ahead and bring down the 4, and end up with 24 instead of 204.

The fix: every time you bring a digit down, something must go in the answer above it, even if that something is a 0. Say it out loud: "31 into 12 doesn't go, so I write a zero."

Mistake 2: Choosing a multiple that's too big or too small

If the subtraction gives a negative number, the guess was too big. If what's left over is bigger than the divisor, the guess was too small.

The fix: go back to the multiples list. And teach one rule: "my leftover must always be smaller than the number I'm dividing by."

Mistake 3: Columns drifting out of line

By the third loop, the numbers have wandered across the page and the child subtracts the wrong digits.

The fix: use squared paper, one digit per square. Most schools do this anyway. If you're working at home, a maths exercise book or even graph paper makes a huge difference.

A 10-minute long division practice routine

Same three steps I use for every skill: watch, copy, practise.

1. Watch: do one example yourself, out loud. Say each step: "Divide. Multiply. Subtract. Bring down."
2. Copy: your child does a very similar one, saying the steps out loud too.
3. Practise: three or four on their own, then check each one by multiplying back.

Only move on when they're getting three in a row right. If one particular step keeps going wrong, it's usually the times tables or the subtraction, so spend a few days on that instead. Ten minutes, a few times a week, is plenty.

Frequently asked questions

What year do children learn long division?

Long division is taught in Year 6 in England. Children learn to divide numbers with up to four digits by a two-digit number. Before that, in Years 4 and 5, they learn short division (the bus stop method) with a one-digit divisor.

What is the difference between long division and short division?

They follow the same steps. In short division the subtraction is done mentally and the remainder is carried as a small digit. In long division the subtraction is written out underneath and the next digit is brought down, which makes it easier with two-digit divisors.

What are the 4 steps of long division?

Divide, multiply, subtract, bring down. Children often remember them with a phrase like "Does McDonald's Sell Burgers?". You repeat the four steps until there are no digits left to bring down.

How do you do long division with remainders?

Work through the steps as normal. Whatever is left at the end is the remainder. It can be written as r 16, as a fraction with the remainder over the divisor (16/24, simplified to 2/3), or as a decimal by adding a decimal point and zeros and carrying on.

Why is long division so hard for children?

Because it uses times tables, subtraction, place value and short division all at once. A gap in any one of them makes long division feel impossible. Writing out the multiples first and practising the missing skill usually fixes it.

Is long division in the Year 6 SATs?

Yes. The arithmetic paper normally includes long division questions worth 2 marks each. Children can use long or short division, but they should always show their working, because a correct method with one small error can still earn a mark.