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division

Long division for confident learners

Break larger division into organised repeated steps.

Quick answer

Long division is a step-by-step method to divide large numbers by breaking the problem into smaller, easier parts. It helps you solve division problems like 847 ÷ 7 by working through one digit at a time.

Learning outcome

By the end of this page, you will be able to use long division to solve bigger division problems with confidence, by breaking them into smaller steps and checking your work carefully. Success signs:
  • You can write out a long division problem clearly
  • You can find the correct answer by working through each step
  • You can check your answer using multiplication
  • You can explain how each step helps you solve the problem

Why this matters

Long division helps you solve division problems that are too big for you to do in your head. It's useful for real-life situations like sharing a large group of items, dividing money, or working out how much time it takes to do something. In school, you'll use long division to solve problems involving larger numbers, and it helps you understand how division works in general.

How it works

Long division uses four main steps to solve a problem:
  1. Divide – Look at the first digit or group of digits of the big number and see how many times the divisor goes into it.
  2. Multiply – Multiply the divisor by the number you found in the first step.
  3. Subtract – Subtract the result from the number you're dividing.
  4. Bring down – Bring down the next digit of the big number and repeat the steps.
Let’s try an example to make this clear.

Examples you can see

Let’s try working out 847 ÷ 7. Step 1: Divide Look at the first digit of 847, which is 8. How many times does 7 go into 8? 7 × 1 = 7 So 7 goes into 8 once. Write 1 above the 8. Step 2: Multiply Multiply 7 × 1 = 7. Write 7 under the 8. Step 3: Subtract Subtract 8 − 7 = 1. Write 1 below the 7. Step 4: Bring down Bring down the next digit, which is 4. Now you have 14. Step 5: Repeat the steps Divide 14 ÷ 7 = 2. Multiply 7 × 2 = 14. Subtract 14 − 14 = 0. Bring down the next digit, 7. Step 6: Final step Divide 7 ÷ 7 = 1. Multiply 7 × 1 = 7. Subtract 7 − 7 = 0. So, 847 ÷ 7 = 121.

Try it as a mini adventure

Adventure: The Treasure Hunt You are on a treasure hunt! The map says, “Find the treasure by dividing 960 coins among 8 friends.” You need to work out how many coins each friend gets. Step 1: Write out the problem: 960 ÷ 8 Step 2: Divide 9 ÷ 8 = 1 (since 8 × 1 = 8) Step 3: Multiply 8 × 1 = 8 Step 4: Subtract 9 − 8 = 1 Step 5: Bring down 6 to make 16 Step 6: Divide 16 ÷ 8 = 2 Step 7: Multiply 8 × 2 = 16 Step 8: Subtract 16 − 16 = 0 Step 9: Bring down 0 Step 10: Divide 0 ÷ 8 = 0 Step 11: Multiply 8 × 0 = 0 Step 12: Subtract 0 − 0 = 0 So, each friend gets 120 coins.

Common mistakes

  • Mistake: Forgetting to bring down the next digit.
    Why it happens: You may get excited and skip a step.
    Fix: Always check that you’ve brought down the next digit before moving on.
  • Mistake: Making a mistake in multiplication.
    Why it happens: You might forget your times tables or make a small error.
    Fix: Use your times tables to double-check your multiplication.
  • Mistake: Not writing numbers in the right place.
    Why it happens: You may get confused with the layout.
    Fix: Keep your numbers lined up neatly in rows.
  • Mistake: Not checking your answer.
    Why it happens: You might think you’re done and skip the final check.
    Fix: Always multiply your answer by the divisor to make sure it matches the original number.

Parent and carer guide

As a parent or carer, you can help your child by:
  • Practising long division with real-life examples like sharing food or dividing money
  • Encouraging your child to write out each step clearly and check their work
  • Reassuring them that mistakes are part of learning and that it's okay to take time
  • Using games or apps to make practice fun
  • Checking that they understand each step before moving on
It's normal for children to get confused at first. Keep the atmosphere calm and supportive. Long division is a skill that takes time to master, so be patient and celebrate small successes!

Practice questions

  1. What is 630 ÷ 9?
  2. What is 728 ÷ 8?
  3. What is 456 ÷ 6?
  4. What is 824 ÷ 4?
  5. What is 576 ÷ 8?
Answers:
  1. 630 ÷ 9 = 70
  2. 728 ÷ 8 = 91
  3. 456 ÷ 6 = 76
  4. 824 ÷ 4 = 206
  5. 576 ÷ 8 = 72

FAQ

What is long division used for?

Long division is used to solve division problems with large numbers. It helps you break down the problem into smaller steps so it’s easier to manage.

Why do we need to bring down the next digit?

We bring down the next digit to continue the division process. It helps us work with the next part of the number and get closer to the final answer.

Can I use long division for any division problem?

Yes, long division works for any division problem, no matter how big the numbers are. It’s just a more organised way of doing it.

How can I check if my answer is correct?

You can check your answer by multiplying the quotient (your answer) by the divisor (the number you divided by). If the result matches the original number, your answer is correct.

Is long division the same as short division?

Short division is a quicker way to do division, but long division is more helpful when you're working with larger numbers or want to be more careful with each step.