Long Division Calculator
Perform long division with step-by-step solution showing the complete process. See also Remainder Calculator and Fraction Calculator.
How to Do Long Division
Long division is a method for dividing large numbers by breaking the problem into a series of simpler steps. You work from left to right through the dividend, determining how many times the divisor fits into each portion. The process involves dividing, multiplying, subtracting, and bringing down the next digit, repeating until all digits have been processed.
Long Division Steps
1. Divide: How many times does divisor fit?
2. Multiply: quotient digit × divisor
3. Subtract: current number − product
4. Bring down: next digit of dividend
5. Repeat until no digits remain
Result: Dividend = Divisor × Quotient + Remainder
Example
1234 ÷ 56
Step 1: 1 ÷ 56 = 0, bring down 2 → 12
Step 2: 12 ÷ 56 = 0, bring down 3 → 123
Step 3: 123 ÷ 56 = 2, 2 × 56 = 112, 123 − 112 = 11
Step 4: Bring down 4 → 114
Step 5: 114 ÷ 56 = 2, 2 × 56 = 112, 114 − 112 = 2
Quotient: 22, Remainder: 2
Check: 56 × 22 + 2 = 1234 ✓
Frequently Asked Questions
What if the divisor is larger than the dividend?
If the divisor is larger than the dividend, the quotient is 0 and the remainder equals the dividend. For example, 5 ÷ 12 = 0 remainder 5.
How do I check my long division answer?
Multiply the quotient by the divisor and add the remainder. The result should equal the dividend: Divisor × Quotient + Remainder = Dividend.
Can long division produce decimals?
Yes. After processing all digits, if there is a remainder, you can add a decimal point and continue dividing by appending zeros. This calculator shows both the integer quotient with remainder and the decimal result.
Why learn long division when calculators exist?
Long division builds understanding of place value, estimation, and the relationship between multiplication and division. It is also the basis for polynomial division in algebra.
Solved Examples — Long Division
Example: 4,578 ÷ 14
Solution:
Step 1: 45 ÷ 14 = 3, 3 × 14 = 42, 45 − 42 = 3
Step 2: Bring down 7 → 37. 37 ÷ 14 = 2, 2 × 14 = 28, 37 − 28 = 9
Step 3: Bring down 8 → 98. 98 ÷ 14 = 7, 7 × 14 = 98, 98 − 98 = 0
Step 4: No remainder
Answer: 327 (Check: 14 × 327 = 4,578 ✓)
Example: $156.75 shared equally among 3 people
Solution:
Step 1: 15675 ÷ 3 (work in cents to avoid decimals)
Step 2: 15 ÷ 3 = 5, 6 ÷ 3 = 2, 7 ÷ 3 = 2 R1, bring down 5 → 15 ÷ 3 = 5
Step 3: Result = 5225 cents = $52.25
Answer: $52.25 each
Example: 2,345 ÷ 23
Solution:
Step 1: 23 ÷ 23 = 1, 1 × 23 = 23, 23 − 23 = 0
Step 2: Bring down 4 → 4. 4 ÷ 23 = 0
Step 3: Bring down 5 → 45. 45 ÷ 23 = 1, 1 × 23 = 23, 45 − 23 = 22
Step 4: Quotient = 101, Remainder = 22
Answer: 101 remainder 22 (Check: 23 × 101 + 22 = 2,345 ✓)
Practice Questions
Try these on your own:
- Calculate 936 ÷ 12 (Answer: 78)
- Calculate 5,432 ÷ 16 (Answer: 339 remainder 8)
- Calculate 7,200 ÷ 45 (Answer: 160)
- A school has 847 students divided into classes of 32. How many full classes and how many students are left? (Answer: 26 classes, 15 students left)
- Calculate 10,000 ÷ 7 (give quotient and remainder) (Answer: 1,428 remainder 4)
- You drive 525 miles in 7.5 hours. What is your average speed? (Answer: 70 mph)
Common Mistakes to Avoid
The most common mistake in long division is estimating the quotient digit incorrectly — guess too high and you get a negative after subtraction (go back and try a smaller digit), guess too low and the remainder is bigger than the divisor (the digit should be larger). Another error is forgetting to write a 0 in the quotient when the divisor does not go into the current number — for example, in 3,024 ÷ 3 = 1,008, not 108. Students also sometimes subtract incorrectly during the process, so always double-check each subtraction. When bringing down digits, bring down ONE digit at a time. The verification step (Divisor × Quotient + Remainder = Dividend) is essential — always use it to check your work.
Key Takeaways
- Long division follows four steps in a cycle: Divide, Multiply, Subtract, Bring Down.
- Always verify: Dividend = Divisor × Quotient + Remainder.
- The remainder must always be less than the divisor. If it's not, your quotient digit is too small.
- Don't forget placeholder zeros in the quotient when the divisor doesn't fit.
- For decimals: add a decimal point to the quotient and append zeros to continue dividing.
- Long division is the foundation for polynomial division, which appears in algebra and calculus.