What Is Long Division?
Long division lets you divide a large number (the dividend) by another number (the divisor) in an organised, written way. The answer is called the quotient; any left-over amount is the remainder.
Division Equation
You can always check: multiply the divisor by the quotient, then add the remainder — you should get the dividend back.
The Four-Step Cycle
- 1
Divide
Look at just enough digits of the dividend to divide. Ask: how many times does the divisor go into this part? - 2
Multiply
Multiply that quotient digit by the divisor and write the result below. - 3
Subtract
Subtract to find the remainder for this step. - 4
Bring down
Bring the next digit of the dividend down next to the remainder, and repeat from Step 1.
Worked Example — Division by a Single Digit
Calculate 8 736 ÷ 4
8 736 ÷ 4 = ?
Thousands: 8 ÷ 4 = 2 → write 2. 2 × 4 = 8. 8 − 8 = 0.
Bring down 7: we now have 07.
Hundreds: 7 ÷ 4 = 1 → write 1. 1 × 4 = 4. 7 − 4 = 3.
Bring down 3: we now have 33.
Tens: 33 ÷ 4 = 8 → write 8. 8 × 4 = 32. 33 − 32 = 1.
Bring down 6: we now have 16.
Ones: 16 ÷ 4 = 4 → write 4. 4 × 4 = 16. 16 − 16 = 0.
Result: 8 736 ÷ 4 = 2 184 (remainder 0)
Check: 2 184 × 4 = 8 736 ✓
Worked Example — Division by a Two-Digit Number
Calculate 4 752 ÷ 16
4 752 ÷ 16 = ?
Start with 47: 47 ÷ 16 = 2 (since 2 × 16 = 32, 3 × 16 = 48 > 47). Write 2. 47 − 32 = 15.
Bring down 5: we now have 155.
155 ÷ 16 = 9 (9 × 16 = 144, 10 × 16 = 160 > 155). Write 9. 155 − 144 = 11.
Bring down 2: we now have 112.
112 ÷ 16 = 7 (7 × 16 = 112). Write 7. 112 − 112 = 0.
Result: 4 752 ÷ 16 = 297 (remainder 0)
Check: 297 × 16 = 4 752 ✓
Remainders
If the final subtraction leaves a non-zero value, that is the remainder. Write it after the quotient using the letter R.
Calculate 100 ÷ 7
100 ÷ 7: 7 goes into 10 once (7), remainder 3. Bring down 0 → 30. 30 ÷ 7 = 4 (28), remainder 2.
Result: 100 ÷ 7 = 14 R 2
Check: 14 × 7 + 2 = 98 + 2 = 100 ✓
Real-World Applications
Real world: sharing equally
48 pupils are divided into groups of equal size for a project. The teacher wants 6 groups. How many pupils are in each group?
48 ÷ 6 = 8 pupils per group.
Real world: finding unit price
A pack of 24 pencils costs 384 cents. What is the cost per pencil?
384 ÷ 24: 24 goes into 38 once (24), remainder 14. Bring down 4 → 144. 144 ÷ 24 = 6.
Each pencil costs 16 cents (0,16 €).
Real world: packing boxes
A factory has 3 250 biscuits to pack into boxes of 12. How many full boxes are made, and how many biscuits are left over?
3 250 ÷ 12 = 270 R 10.
270 full boxes, with 10 biscuits left over.
Common Mistakes
- Forgetting to bring down the next digit after subtracting
- Placing the quotient digit in the wrong column
- Choosing a quotient digit that is too large (the product exceeds the partial dividend)
- Forgetting to write a 0 in the quotient when the divisor does not go into the partial dividend
Practice Problems
Calculate 5 928 ÷ 8.
Show answer
A 2 856-kilometre journey is split into 14 equal daily stages. How long is each stage?