Long Division Calculator
Long Division Calculator
Perform long division with step-by-step explanations
The number you want to divide
The number you're dividing by
How to Do Long Division: Complete Guide
Long division is a method for dividing large numbers by breaking the problem into smaller, manageable steps. It systematically divides the dividend (the number being divided) by the divisor (the number you're dividing by) to find the quotient (the answer) and remainder.
Quick Answer
Long division formula: Dividend ÷ Divisor = Quotient + Remainder/Divisor. For example, 156 ÷ 12 = 13 remainder 0, which equals 13.
Long Division Steps
The four essential steps repeated until the division is complete.
Step-by-Step Process:
- 1Divide: Look at the first digit(s) of the dividend. Find how many times the divisor goes into this number. Write this digit above the division line as part of your quotient.
- 2Multiply: Multiply the quotient digit by the divisor. Write this product below the dividend digits you just divided. This shows how much you're "taking away."
- 3Subtract: Subtract the product from the dividend digits above it. This gives you the remainder for this step. The result should always be smaller than the divisor.
- 4Bring Down: Bring down the next digit from the dividend to the right of your remainder. Repeat the process with this new number until all digits have been used.
Division Terminology
Dividend
The number being divided. In 156 ÷ 12, the dividend is 156. This is the total amount you're splitting up.
Divisor
The number you're dividing by. In 156 ÷ 12, the divisor is 12. This tells you how many equal groups to make.
Quotient
The answer to the division problem. In 156 ÷ 12 = 13, the quotient is 13. This is how many items per group.
Remainder
What's left over after division. If 157 ÷ 12 = 13 R1, the remainder is 1. This is what doesn't divide evenly.
Common Long Division Challenges
Zeros in the Quotient
When the divisor doesn't go into the current dividend digits, place a 0 in the quotient and bring down the next digit. Example: 1008 ÷ 4 requires placing zeros in the quotient.
Estimating Quotient Digits
Use multiplication tables and estimation to find the right quotient digit. If your estimate is too big, the subtraction will be negative - adjust down and try again.
Large Numbers
Break large numbers into manageable chunks. Focus on just the digits you need for each step, and keep your work organized in neat columns.
Decimal Results
When there's a remainder, you can continue dividing by adding decimal places and zeros to find the decimal quotient.
Worked Examples
Example 1: 84 ÷ 4
Example 2: 156 ÷ 12
Division Tips and Strategies
Success Strategies
- Check your work: Multiply your quotient by the divisor and add the remainder. You should get the original dividend.
- Estimate first: Round numbers to estimate the approximate answer before doing the exact calculation.
- Know your multiplication tables: Strong multiplication skills make finding quotient digits much faster.
- Keep work organized: Line up digits carefully and keep your working neat to avoid errors.
- Practice with easier numbers: Start with single-digit divisors before moving to two-digit divisors.
- Use estimation to check: If 156 ÷ 12, estimate 150 ÷ 10 = 15, so the answer should be close to 15.
Types of Division Results
Exact Division
- • No remainder (divides evenly)
- • Quotient is a whole number
- • Example: 84 ÷ 4 = 21
- • Verification: 21 × 4 = 84 ✓
Division with Remainder
- • Has a remainder (doesn't divide evenly)
- • Can express as mixed number or decimal
- • Example: 85 ÷ 4 = 21 R1
- • As decimal: 85 ÷ 4 = 21.25
Real-World Applications
Sharing and Distribution
Dividing items equally among groups. If you have 156 cookies and 12 people, each person gets 13 cookies.
Time and Scheduling
Calculating how many complete time periods fit into a duration. 156 minutes ÷ 12 minutes per task = 13 complete tasks.
Measurement and Units
Converting between units. 156 inches ÷ 12 inches per foot = 13 feet exactly.
Money and Finance
Dividing costs or calculating unit prices. $156 ÷ 12 items = $13 per item.
Common Mistakes to Avoid
Alignment Errors
Keep digits aligned in proper columns. Misaligned numbers lead to incorrect calculations and wrong answers.
Forgetting to Bring Down
Always bring down the next digit before starting a new division step. Skipping this step leads to incomplete solutions.
Incorrect Quotient Estimation
If subtraction gives a negative result, your quotient digit is too large. Reduce it and try again.
Not Checking the Answer
Always verify: (Quotient × Divisor) + Remainder = Dividend. This catches most calculation errors.
Frequently Asked Questions
Why do we use long division instead of a calculator?
Long division teaches number sense, place value understanding, and problem-solving skills. It helps you understand what division actually means and builds mental math abilities.
What if the divisor is larger than the dividend?
When the divisor is larger than the dividend, the quotient is 0 and the remainder equals the dividend. For example, 7 ÷ 12 = 0 remainder 7.
How do I know when to stop dividing?
Stop when you've used all digits from the dividend. If there's a remainder, you can continue with decimal places by adding zeros and decimal points.
What's the difference between terminating and repeating decimals?
Terminating decimals have a finite number of decimal places (like 0.25). Repeating decimals continue forever with a pattern (like 0.333...). This depends on the prime factors of the divisor.
Can I use long division with decimals?
Yes, but it's easier to eliminate decimals first. Multiply both dividend and divisor by the same power of 10 to make them whole numbers, then divide normally.
Related Mathematical Tools
Long Division Calculator
Perform long division with step-by-step explanations
The number you want to divide
The number you're dividing by