Maths
How do you do long division?
Quick answer
Long division splits a big number into equal groups by repeating four steps: divide, multiply, subtract, bring down. Work from the left, one digit at a time.
In one sentence
Long division is a written method for dividing large numbers, one digit at a time, using the same four steps again and again.
Explained
Short division works when you can do the sums in your head. Long division is for bigger numbers, where you write every step down. The steps repeat in a loop. A common way to remember them is Divide, Multiply, Subtract, Bring down.
Let us work out 756 ÷ 6.
Step by step
- Divide.How many times does 6 go into 7? Once. Write 1 above the 7.
- Multiply.1 × 6 = 6. Write 6 under the 7.
- Subtract.7 − 6 = 1.
- Bring down.Bring down the next digit, 5, to make 15.
Now go round again. 6 goes into 15 twice (2 × 6 = 12), and 15 − 12 = 3. Bring down the 6 to make 36. 6 goes into 36 exactly six times, and 36 − 36 = 0. The answer on top is 126. Check with multiplication: 6 × 126 = 756. Good.
pencil
notebook
ruler
If the last subtraction leaves a number, that is the remainder. For 487 ÷ 4 you get 121 with 3 left over, written as 121 r 3. Read more in remainders. Division is the opposite of multiplication, so your times tables do most of the work. Writing out the first few multiples of the divisor (6, 12, 18, 24 …) at the side makes each step faster.
Examples
| Sum | Answer | Check |
|---|---|---|
| 96 ÷ 8 | 12 | 8 × 12 = 96 |
| 756 ÷ 6 | 126 | 6 × 126 = 756 |
| 618 ÷ 6 | 103 | 6 × 103 = 618 |
| 487 ÷ 4 | 121 r 3 | 4 × 121 + 3 = 487 |
Common mistakes
- Forgetting a zero in the answer. In 618 ÷ 6, 6 cannot go into 1, so write 0 and carry on.
- Not bringing down. After you subtract, always bring down the next digit before you divide again.
- Subtraction slips. The remainder must always be smaller than the number you are dividing by. If it is bigger, your answer digit was too small.
Quick quiz
Long division
Check what you know with 4 quick questions.
Question 1 of 4
What are the four steps of long division, in order?
Practise it
Try it
Division practice
Practise it step by step in a full course: Grade 6 Maths
For grown-ups
Related topics
Division
Division is sharing into equal groups, or finding how many groups fit. The sign is ÷, so 12 ÷ 3 = 4. The answer is called the quotient.
Remainders
A remainder is what is left over when one number does not divide exactly into another. In 17 ÷ 5 = 3 remainder 2, the 2 is left over after making three groups of 5.
Times tables
Times tables are lists of the multiplication facts for a number, such as 3 × 1 = 3 up to 3 × 12 = 36. Knowing them by heart speeds up almost all later maths.
The 24-hour clock
The 24-hour clock counts the hours from 00:00 at midnight to 23:59, so there is no am or pm. For afternoon times, add 12: 3 pm is 15:00.
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
3D shapes
3D shapes are solid shapes with length, width and height, like cubes, spheres, cylinders and pyramids. They have faces, edges and vertices.