Long Division Calculator
Quotient, remainder, and decimal for any division.
What it does
Long division splits a dividend into whole groups of the divisor, reporting how many full groups fit with what spills over. The quotient counts groups, the remainder keeps the leftover, and the decimal continues past it.
The tool above takes both numbers. It returns the quotient with remainder plus the decimal and the multiply back check beside them.
The default 154 over 7 divides evenly: 22 remainder 0 (22 decimal). A messier 100 over 3 gives 33 remainder 1 (33.3333), showing all three faces at once.
Definitions follow Khan Academy division units with the same quotient remainder language in LibreTexts math references. Both treat division by zero as undefined, rejected here.
How to use
- Enter the dividend (the number inside).
- Enter the divisor (the number outside).
- Read quotient with remainder first.
- Read decimal for the continued value.
- Multiply back to verify homework.
Formula
- trunc
- Whole groups, dropping the fraction.
- remainder
- Leftover below one more group.
- check
- Groups times divisor plus leftover rebuilds.
Truncation heads toward zero for negatives, matching standard remainder behavior. Decimals display four places; repeating tails round at the fourth.
Worked example
Example: 154 / 7
Defaults: 154 inside, 7 outside.
- Fit: 7 goes into 15 twice (14), into 14 twice: 22 total.
- Remainder: 154 - 22 x 7 = 154 - 154 = 0.
- Decimal: 22 exactly.
- Check: 22 x 7 + 0 = 154 back.
- Tool shows 22 r 0, 22, check line.
Reference table
| Problem | Quotient | Decimal |
|---|---|---|
| 154 / 7 | 22 r 0 | 22 |
| 100 / 3 | 33 r 1 | 33.3333 |
| 1000 / 8 | 125 r 0 | 125 |
| 17 / 5 | 3 r 2 | 3.4 |
Limits
- Truncation toward zero for negatives.
- Four decimal display; tails round there.
- Numbers cap under a trillion.
- Fractions need the fraction page instead.
Common mistakes
- Dividing by zero and expecting an answer.
- Dropping the remainder from the check.
- Reading 33.3333 as exact instead of rounded.
- Swapping dividend with divisor.
- Stopping before verifying by multiplying back.
Try it yourself
Quick checks. Answers sit tucked under each question.
100 / 3?
33 r 1, decimal 33.3333.
1000 / 8?
125 r 0, decimal 125.
Check for 100 / 3?
33 x 3 + 1 = 100 back.
Questions
What is 154 divided by 7?
22 remainder 0: it divides evenly.
Quotient vs decimal?
Quotient counts whole groups with remainder; decimal continues past it.
How do I check?
Multiply quotient by divisor, add remainder: must rebuild the dividend.
Why remainder?
Leftovers below one full group: 100/3 leaves 1.
Can I divide by zero?
No. It is undefined and rejected here.
Negative dividends?
Truncation heads toward zero; check the check line.