Long Division Examples: Step-by-Step Guide for Students & Teachers
Master long division step-by-step with clear worked examples, bus stop method diagrams, easy-to-hard practice problems, decimal division rules, and common mistakes to avoid.
Long Division Examples: Step-by-Step Guide for Students & Teachers
Long division is one of those math skills that can feel overwhelming at first — but once you break it down step by step, it actually makes perfect sense. Whether you are a student learning long division for the first time, a teacher preparing classroom lessons, or a parent helping with math homework, this guide has everything you need.
In this article, you will find step-by-step long division examples with clear explanations, easy, medium, and hard practice problems, common division mistakes and how to avoid them, real-world word problems, practice questions with full worked answers, and direct links to our interactive math tools.
Try Long Division CalculatorGet instant step-by-step long division work with remainders and decimal answers.What is Long Division?
Long division is a standard algorithm for dividing one number (the dividend) by another number (the divisor) when the numbers are too large for mental math. It breaks a complex division problem into a series of smaller, manageable calculation steps.
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| Term | Definition | Example (175 ÷ 3) |
|---|---|---|
| Dividend | The number being divided | 175 |
| Divisor | The number you divide by | 3 |
| Quotient | The answer (whole number part) | 58 |
| Remainder | The amount left over | 1 |
The 5 Steps of Long Division
Long division follows a simple 5-step process that repeats sequentially until the problem is solved. The simple mnemonic to remember is: Divide, Multiply, Subtract, Bring Down, Repeat!
The 5-Step Long Division Cycle
Follow these five steps sequentially until no dividend digits remain.
1. Divide
How many times does the divisor go into the current working digit(s)?
2. Multiply
Multiply the divisor by the quotient digit you just wrote above.
3. Subtract
Subtract the product from the current working digit(s).
4. Bring Down
Bring down the next digit from the dividend to form a new working number.
5. Repeat
Start again from Step 1 until there are no more digits to bring down.
Always check that your subtraction result is smaller than the divisor before bringing down.
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| Step | Action | What to Do |
|---|---|---|
| Step 1 | Divide | How many times does the divisor go into the current digit(s)? |
| Step 2 | Multiply | Multiply the divisor by the number you just wrote. |
| Step 3 | Subtract | Subtract the product from the current digit(s). |
| Step 4 | Bring Down | Bring down the next digit from the dividend. |
| Step 5 | Repeat | Start again from Step 1 until there are no more digits. |
How to Set Up Long Division (Bus Stop Method)
The bus stop method (also known as the division bracket) is the standard visual layout for long division. The divisor sits outside the bracket on the left, the dividend sits inside under the roof, and the quotient is written on top.
Step-by-Step Worked Example (175 ÷ 3)
Let us divide 175 by 3 step-by-step using our 5-step cycle.
- Step 1: Set up the bracket: 3 ) 175
- Step 2: Divide first digit (1): 3 does not go into 1, so look at the first two digits (17).
- Step 3: 3 goes into 17 five times (3 × 5 = 15). Write 5 on top above 7.
- Step 4: Multiply 3 × 5 = 15. Write 15 below 17.
- Step 5: Subtract 17 − 15 = 2.
- Step 6: Bring down the next digit (5). Now you have 25.
- Step 7: Divide again: 3 goes into 25 eight times (3 × 8 = 24). Write 8 on top above 5.
- Step 8: Multiply 3 × 8 = 24. Write 24 below 25.
- Step 9: Subtract 25 − 24 = 1. There are no more digits to bring down.
How to Check Your Answer
Always verify your long division work using the inverse multiplication check formula. Multiplying the quotient by the divisor and adding the remainder must yield the original dividend.
Easy Long Division Examples
Example 1: 180 ÷ 12 (Word Problem: Egg Trays)
Question: Eggs are put in trays of 12. Each box contains 180 eggs. How many trays are in each box?
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| Step | Action | Calculation |
|---|---|---|
| 1 | Set up bracket | 12 ) 180 |
| 2 | 12 goes into 18? | 1 time (1 × 12 = 12) |
| 3 | Subtract | 18 − 12 = 6 |
| 4 | Bring down 0 | 60 |
| 5 | 12 goes into 60? | 5 times (5 × 12 = 60) |
| 6 | Subtract | 60 − 60 = 0 |
| 7 | Final Answer | 15 trays in each box (Check: 15 × 12 = 180) |
Example 2: 504 ÷ 21 (Word Problem: Charity Donations)
Question: A lottery donates £504 to 21 different charities. How much does each charity get?
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| Step | Action | Calculation |
|---|---|---|
| 1 | Set up bracket | 21 ) 504 |
| 2 | 21 goes into 50? | 2 times (2 × 21 = 42) |
| 3 | Subtract | 50 − 42 = 8 |
| 4 | Bring down 4 | 84 |
| 5 | 21 goes into 84? | 4 times (4 × 21 = 84) |
| 6 | Subtract | 84 − 84 = 0 |
| 7 | Final Answer | Each charity gets £24 (Check: 24 × 21 = 504) |
Medium Long Division Examples
Example 3: 8,051 ÷ 83 (SATs Exam Question)
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| Step | Action | Calculation |
|---|---|---|
| 1 | Set up bracket | 83 ) 8051 |
| 2 | 83 goes into 8? | No (0) → write 0 above 8 |
| 3 | 83 goes into 80? | No (0) → write 0 above 0 |
| 4 | 83 goes into 805? | 9 times (9 × 83 = 747) |
| 5 | Subtract | 805 − 747 = 58 |
| 6 | Bring down 1 | 581 |
| 7 | 83 goes into 581? | 7 times (7 × 83 = 581) |
| 8 | Subtract | 581 − 581 = 0 |
| 9 | Final Answer | 8,051 ÷ 83 = 97 (Check: 97 × 83 = 8,051) |
Example 4: 1,000 ÷ 34 (Word Problem: Paper Booklets)
Question: Adam is making booklets. Each booklet must have 34 sheets of paper. He has 2 packets of paper with 500 sheets each (1,000 total sheets). How many complete booklets can Adam make?
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| Step | Action | Calculation |
|---|---|---|
| 1 | Set up bracket | 34 ) 1000 |
| 2 | 34 goes into 100? | 2 times (2 × 34 = 68) |
| 3 | Subtract | 100 − 68 = 32 |
| 4 | Bring down 0 | 320 |
| 5 | 34 goes into 320? | 9 times (9 × 34 = 306) |
| 6 | Subtract | 320 − 306 = 14 |
| 7 | Final Answer | 29 complete booklets (14 sheets left over) |
Hard Long Division Examples
Example 5: 4,923 ÷ 37 (Factory Teddy Bears)
Question: A factory makes 4,923 teddy bears, and the bears are packed in boxes of 37. How many bears are left over?
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| Step | Action | Calculation |
|---|---|---|
| 1 | 37 goes into 49? | 1 time (1 × 37 = 37) |
| 2 | Subtract | 49 − 37 = 12 |
| 3 | Bring down 2 | 122 |
| 4 | 37 goes into 122? | 3 times (3 × 37 = 111) |
| 5 | Subtract | 122 − 111 = 11 |
| 6 | Bring down 3 | 113 |
| 7 | 37 goes into 113? | 3 times (3 × 37 = 111) |
| 8 | Subtract | 113 − 111 = 2 |
| 9 | Final Answer | 133 R2 → 2 teddy bears are left over. |
Example 6: 427 ÷ 15 (Castle Visit Adult Escorts)
Question: 427 children visit a castle in groups of 15. One group has fewer than 15. Every group has one adult escort. How many adults will need to go?
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| Step | Action | Calculation |
|---|---|---|
| 1 | Divide 427 ÷ 15 | 28 R7 |
| 2 | Full groups | 28 groups of 15 children |
| 3 | Partial group | 1 group with 7 children |
| 4 | Total groups | 28 + 1 = 29 groups |
| 5 | Adults required | 29 adults needed (1 adult per group) |
Example 7: 1,176 ÷ 392 (Apple Boxes Ordering)
Question: A grocer needs to order 1,176 apples. Apples are sold in boxes containing 28 trays, with 14 apples on each tray. How many boxes of apples does the grocer need to order?
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| Step | Action | Calculation |
|---|---|---|
| 1 | Calculate apples per box | 28 trays × 14 apples = 392 apples per box |
| 2 | Set up bracket | 392 ) 1176 |
| 3 | 392 goes into 1176? | 3 times (3 × 392 = 1176) |
| 4 | Subtract | 1176 − 1176 = 0 |
| 5 | Final Answer | The grocer needs to order 3 boxes of apples. |
Long Division with Decimal Answers
Sometimes you need an exact decimal quotient instead of a remainder. To continue dividing past the decimal point, add a decimal point to both the dividend and quotient, then bring down trailing zeros.
Example 8: 22 ÷ 4 = 5.5
- Step 1: Normal division: 4 goes into 22 four times (5 × 4 = 20) with remainder 2.
- Step 2: Add decimal point: 22.0 ÷ 4. Bring down 0 to make 20.
- Step 3: 4 goes into 20 five times (5 × 4 = 20) with remainder 0.
- Answer: 22 ÷ 4 = 5.5 (Check: 5.5 × 4 = 22).
Example 9: 10 ÷ 3 = 3.333... (Repeating Decimal)
Dividing 10 by 3 results in a repeating remainder of 1. The quotient is 3.333... (a non-terminating repeating decimal). You can easily convert repeating decimals into exact simplified fractions using our Decimal to Fraction Calculator or perform fraction operations with our Fraction Calculator.
Common Long Division Mistakes & How to Avoid Them
Common Long Division Traps vs. Correct Strategies
Review these frequent mistakes to ensure error-free calculations.
Common Mistakes to Avoid
Frequent traps students and teachers encounter
- Forgetting to bring down the next digit from dividend
- Multiplying by an incorrect quotient digit
- Misplacing quotient digits over wrong column
- Forgetting 0 in quotient when divisor won't fit
- Stopping early when a remainder exists
- Not checking work with inverse multiplication
Correct Strategies to Follow
Proven step-by-step habits for accurate division
- Check if dividend digits remain before finishing
- Verify product is <= current working number
- Align quotient digits directly above active column
- Always write 0 in quotient if divisor > working number
- Add decimal point and trailing zeros for decimals
- Verify using: Dividend = (Divisor * Quotient) + Remainder
Always write down multiples and line up digits neatly before dividing.
Top Tips for Long Division Success
- List 9 multiples of the divisor before you start — Saves time and prevents mental arithmetic errors.
- Line up place values carefully — Each quotient digit goes directly above its corresponding dividend digit.
- Write clearly and neatly — Neat vertical alignment prevents subtraction mistakes.
- Always include 0 when needed — If the divisor cannot fit into a digit, write 0 in the quotient.
- Double-check subtraction steps — Subtraction errors are the #1 cause of wrong long division answers.
- Use inverse multiplication to verify — Multiply quotient by divisor and add remainder to check.
- Take your time — Long division is a structured algorithm; don't rush steps.
- Use interactive calculators to practice — Check your work step-by-step with online tools.
Practice Questions (With Answers)
Test your long division skills with these 7 practice questions:
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| Question # | Problem Description | Answer |
|---|---|---|
| Question 1 | Divide 256 ÷ 7 | 36 R4 (or 36.571...) |
| Question 2 | Divide 1,024 ÷ 8 | 128 |
| Question 3 | Divide 3,456 ÷ 12 | 288 |
| Question 4 | Divide 5,000 ÷ 25 | 200 |
| Question 5 | Divide 10,000 ÷ 13 | 769 R3 (or 769.23...) |
| Question 6 | 1,000 students divided into groups of 24 | 41 groups, 16 students left over |
| Question 7 | 2,500 widgets packed in boxes of 48 | 52 boxes, 4 widgets left over |
Related Math Calculators & Guides
Explore our suite of free math calculators and guides for all your arithmetic and mathematical workflows:
- Long Division Calculator — Calculate long division step-by-step with remainders and decimals.
- Fraction Calculator — Add, subtract, multiply, and divide fractions easily.
- Decimal to Fraction Calculator — Convert terminating and repeating decimals into simplified fractions.
- Standard Form Converter — Convert large numbers and division outputs into scientific notation.
- Average Calculator — Compute dataset mean, weighted average, and GPA scores.
- Rounding Calculator — Round numbers to nearest whole number, tenth, or hundredth.
What is long division?
Long division is a standard mathematical method of dividing one number by another when numbers are too large for mental math. It breaks division into smaller steps: divide, multiply, subtract, bring down, repeat.
What are the 5 steps of long division?
The 5 steps of long division are: Divide, Multiply, Subtract, Bring Down, Repeat. This cycle continues until no dividend digits remain.
What is the dividend in long division?
The dividend is the number being divided. In 175 ÷ 3, the dividend is 175.
What is the divisor in long division?
The divisor is the number you divide by. In 175 ÷ 3, the divisor is 3.
What is the quotient in long division?
The quotient is the result of the division problem. In 175 ÷ 3 = 58 R1, the whole number quotient is 58.
What is a remainder in long division?
A remainder is the integer amount left over when the dividend cannot be divided evenly by the divisor. In 175 ÷ 3 = 58 R1, the remainder is 1.
How do I check my long division answer?
Use the verification formula: Dividend = (Divisor × Quotient) + Remainder. If the result matches your original dividend, your division is correct.
How do I do long division with decimals?
After reaching the last whole digit, place a decimal point in both the quotient and dividend, add trailing zeros, and continue the 5-step cycle until the desired decimal precision is reached.
Why do some long division answers have repeating decimals?
Some division problems never resolve to zero remainder because the divisor and remainder form a repeating fractional cycle (e.g. 10 ÷ 3 = 3.333...).
What happens if the divisor is larger than the first digit?
Write 0 above that digit in the quotient and combine it with the next digit of the dividend (e.g. 3 into 1 is 0, so evaluate 3 into 17).
What if the divisor is 0?
Division by zero is mathematically undefined. In software and calculators, dividing by zero produces an error.
Why do we learn long division if we have calculators?
Learning long division builds numerical fluency, spatial reasoning, understanding of place values, and algorithmic thinking required for advanced math.
How can I practice long division?
Use our Long Division Calculator to check your work step-by-step, try the practice problems in this guide, or complete practice worksheets.
What age group is long division for?
Long division is typically introduced in 4th–5th grade in the US (ages 9–11) and Year 5–6 in the UK national curriculum.
Is long division still taught in schools?
Yes, long division remains a core component of elementary and middle school mathematics curricula worldwide.
Written by
Do The Calculation Team
Do The Calculation Editorial Board
The Do The Calculation Editorial Board is comprised of software engineers, finance analysts, and technical contributors focused on building clean, accurate, and easy-to-use calculator tools.
Reviewed & Verified By
Dr. Elena Rostova, PhD
Mathematics Advisor
Professor of mathematics with 20+ years of teaching experience. Dr. Rostova oversees the formulas, proofs, and algorithms behind our math division tools, fractions, logarithms, and scientific equations.