Long division

National Curriculum: expected secure by the end of Year 6.

What it is

Long division is the written method for dividing by a two-digit number. It uses the same layout as short division, but each step is written out in full underneath: how many times the divisor fits, the multiplication, the subtraction to find what is left, and the next digit brought down. The working moves down the page instead of being carried as small digits.

The name catches parents out. Many adults call any division in that layout long division, but schools separate two methods: short division, from Year 4, carries each leftover as a small digit and suits one-digit divisors, where every step is a known table fact; long division, from Year 6, writes the subtraction out, which gives room for a two-digit divisor: how many 23s are in 117 is not a table fact, so the working cannot be held as small carried digits.

For 2647 ÷ 23, start by listing multiples of 23: 23, 46, 69, 92, 115. Then work digit by digit. 23 into 26 goes 1 time; write 1 on top, subtract 23 from 26 to leave 3, bring down the 4 to make 34. 23 into 34 goes 1 time; subtract 23 to leave 11, bring down the 7 to make 117. 23 into 117 goes 5 times, because 5 × 23 = 115; subtract to leave 2. Nothing is left to bring down, so the answer is 115 remainder 2.

When children learn it

Long division is taught in Year 6 (ages 10 to 11), alongside long multiplication — the written methods the primary curriculum introduces last. It stands directly on earlier skills: short division from Year 4, times-table recall to choose each multiple, and column subtraction inside every step. A Year 6 child stuck on long division usually has the real gap in one of those three.

What it looks like when it goes wrong

These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.

• The wrong multiple chosen. How many 23s in 117 answered with 4, leaving 25 — a remainder bigger than the divisor, which is the signal to go one more — or with 6, overshooting so the subtraction cannot be done. Without a multiples list written down, each step is a guess at an unfamiliar table.
• The subtraction inside a step goes wrong. Every step of long division ends in a column subtraction, and the classic subtraction errors surface there: 452 − 368 done digit by digit as smaller-from-larger gives 116 instead of 84, and every digit of the answer after that step is wrong. This is a column-subtraction gap showing through long division.
• The columns drift. The brought-down digit lands in the wrong column, or an answer digit is written over the wrong place, so a correct sequence of steps still produces a wrong answer. Squared paper, one digit per square, removes most of these.
• The remainder is written down but not interpreted. 2647 ÷ 23 answered as 115 remainder 2 whatever the question asked. In Year 6 the remainder often has to become a fraction — 115 and 2/23 — or the division continues into decimal places, and in a word problem it can mean rounding up. Always writing the remainder shows that step is a habit rather than a decision about the question.

How to help at home

• Have them list the first five multiples of the divisor before starting — for 23: 23, 46, 69, 92, 115. Every how-many-times-does-it-go step becomes a comparison against the list instead of a guess.
• If you learned a different layout at school, resist teaching it — two methods running at once in Year 6 tend to interfere. Ask your child to talk you through their school's steps instead; explaining them is practice, and it shows you where the method breaks.
• Check the answer by multiplying back: 115 × 23 = 2645, and 2645 + 2 = 2647. The inverse check catches most wrong answers and exercises the multiplication the method depends on.
• When it keeps going wrong, find which part fails — the multiple chosen (times tables), the subtraction, or the layout — and practise that part on its own. Repeating whole long divisions gives more practice at the step that is already wrong.