Long division calculator with step-by-step work
Enter a whole-number dividend and nonzero divisor. HitEquals reports quotient and remainder, then lists each partial dividend, quotient digit, product and subtraction.
Inputs used by this calculator
Long Division Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Dividend | 2,596 | 0 to 999999999999999 | Supplies the dividend quantity used by the published equation or result breakdown. |
| Divisor | 4 | 1 to 999999999999999 | Supplies the divisor quantity used by the published equation or result breakdown. |
Long division steps
Read the dividend from left to right. Divide the current partial dividend, write the next quotient digit, multiply, subtract and bring down the next digit.
Quotient and remainder
The quotient counts complete groups. The remainder is what stays after those groups and must be smaller than the divisor.
dividend = divisor × quotient + remainderZeros in the quotient
When a partial dividend is smaller than the divisor after the quotient has started, write a zero in that quotient position before bringing down again.
Check the answer
Multiply divisor by quotient and add remainder. The result must equal the original dividend.
Scope and decimals
This page shows exact whole-number division. A decimal quotient equals quotient plus remainder divided by divisor and is included in the result details.
How to interpret a remainder
A remainder can stay as a whole-number remainder, become a fraction over the divisor or continue into decimal places. The appropriate form depends on the question: 17 objects placed into groups of 5 gives 3 full groups with 2 left, while 17÷5 as a measurement is 3.4.
Common long-division mistakes
Missing a zero in the quotient changes every later place value. Other common errors include multiplying by the entire quotient instead of the current digit, subtracting incorrectly and bringing down more than one digit.
- Estimate one quotient digit.
- Multiply that digit by the divisor.
- Subtract and confirm the remainder is smaller than the divisor.
- Bring down exactly one next digit.
Long division cycle
| Action | Question |
|---|---|
| Divide | How many whole times? |
| Multiply | Quotient digit × divisor |
| Subtract | Find the new remainder |
| Bring down | Append the next digit |
Ways to express the same division result
| Form | 17 ÷ 5 | Typical use |
|---|---|---|
| Quotient and remainder | 3 R 2 | Grouping whole objects |
| Mixed number | 3 2/5 | Exact arithmetic |
| Improper fraction | 17/5 | Algebra |
| Decimal | 3.4 | Measurement |
Frequently asked questions
What is the dividend?
It is the number being divided.
What is the divisor?
It is the nonzero number dividing the dividend.
What is a remainder?
It is the amount left after all complete divisor groups are counted.
How do I check long division?
Multiply divisor by quotient and add the remainder.
Does this accept decimals?
No. This step display is for nonnegative whole numbers.
Why must the remainder be smaller than the divisor?
If it were at least as large, one more complete divisor group could be included in the quotient.
When should I write a zero in the quotient?
Write zero when the current partial dividend is smaller than the divisor after quotient digits have already begun.
What to keep in mind
Whole nonnegative integers only. The table follows base-10 digits from left to right.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.