How to divide two numbers using long division
Long division is an essential written method for dividing large numbers accurately without a calculator: a skill tested directly in GCSE and IGCSE Maths exams. This page explains the D-M-S-B cycle (Divide, Multiply, Subtract, Bring down), shows you how to handle remainders as fractions or decimals, and walks through step-by-step worked examples from simple cases up to four-digit dividends. At the bottom, the auto-marked practice rooms give you instant feedback so you can build speed and confidence before exam day.
Key Terminology
| Term | Meaning |
|---|---|
| Dividend | The number being divided. In \(408 \div 12\), the dividend is \(408\). |
| Divisor | The number you are dividing by. In \(408 \div 12\), the divisor is \(12\). |
| Quotient | The result of the division. In \(408 \div 12 = 34\), the quotient is \(34\). |
How to Do Long Division (The D-M-S-B Cycle)
Repeat this four-step cycle for each digit of the dividend:
- Divide: how many times does the divisor go into the current number?
- Multiply: multiply that answer by the divisor and write it below.
- Subtract: subtract to find the remainder.
- Bring down: bring down the next digit of the dividend and repeat.
If a remainder is left at the end, express it as a fraction (remainder over divisor) or continue as a decimal by bringing down zeros.
Core Ideas
Worked Examples
💡 Example 1: Exact Answer
\(432 \div 16\)
Step by step
- 16 into 43 goes 2 times (2 times 16 is 32). Subtract: 43 minus 32 is 11.
- Bring down 2 to make 112.
- 16 into 112 goes 7 times (7 times 16 is 112). Subtract: 0.
- Answer: \(432 \div 16 = 27\).
💡 Example 2: With Remainder
\(259 \div 12\)
Step by step
- 12 into 25 goes 2 times (2 times 12 is 24). Subtract: 25 minus 24 is 1.
- Bring down 9 to make 19.
- 12 into 19 goes 1 time (1 times 12 is 12). Subtract: 19 minus 12 is 7.
- Remainder 7. Answer: \(21\tfrac{7}{12}\) or \(21.58\) (2 d.p.).
💡 Example 3: Decimal Answer
\(85 \div 4\)
Step by step
- 4 into 8 is 2. Subtract: 0.
- Bring down 5. 4 into 5 is 1 remainder 1.
- Place the decimal point. Bring down 0 to make 10.
- 4 into 10 is 2 remainder 2. Bring down 0 to make 20.
- 4 into 20 is 5. Answer: \(21.25\).
💡 Example 4: Larger Divisor
\(1547 \div 23\)
Step by step
- 23 into 154 goes 6 times (6 times 23 is 138). Subtract: 154 minus 138 is 16.
- Bring down 7 to make 167.
- 23 into 167 goes 7 times (7 times 23 is 161). Subtract: 167 minus 161 is 6.
- Answer: \(67\tfrac{6}{23}\) or \(67.26\) (2 d.p.).
🔑 Key Points
- Always estimate first; check your answer is the right order of magnitude.
- Follow D-M-S-B strictly for every digit.
- If the divisor is larger than the current number, write 0 in the quotient and bring down the next digit.
- Express remainders as fractions \(\frac{r}{d}\) or continue with zeros for a decimal answer.
- Check by multiplying your answer by the divisor; you should get back to the dividend.
⚠️ Common Pitfalls
- Forgetting to write a 0 in the quotient when the divisor is too large to divide into the current number.
- Misaligning digits; keep columns neat or use squared paper.
- Stopping too early; always bring down every digit.
- Forgetting to add a decimal point before bringing down zeros for a decimal answer.
- Not checking the answer by multiplying back.