A long division calculator divides a whole number by another and shows the quotient and the remainder. 125 ÷ 4 is 31 remainder 1, since 4 × 31 + 1 = 125.
On this page
How to use the long division calculator
- Enter the dividend, the number being divided.
- Enter the divisor, which cannot be 0.
- Read the quotient and remainder.
How the long division calculator works
The long division calculator divides one whole number, the dividend, by another, the divisor, and gives a whole-number quotient and a remainder. The answer always checks out as:
- dividend = divisor × quotient + remainder
- The remainder is smaller than the divisor in size
Enter whole numbers; the divisor cannot be 0. Decimal inputs give a decimal quotient, and whole numbers also show the decimal and mixed number.
Long division calculator worked example
Divide 125 by 4 step by step. 4 goes into 12 three times (12), leaving 0; bring down the 5. 4 goes into 5 once (4), leaving 1. The quotient is 31 and the remainder is 1, written 31 R 1. Check: 4 × 31 + 1 = 125. As a decimal, 1 ÷ 4 = 0.25, so 125 ÷ 4 = 31.25. The long division calculator shows 31 R 1.
| Dividend | Divisor | Quotient | Remainder | Decimal |
|---|---|---|---|---|
| 125 | 4 | 31 | 1 | 31.25 |
| 365 | 12 | 30 | 5 | 30.4167 |
| 1,000 | 7 | 142 | 6 | 142.857 |
| 9,876 | 32 | 308 | 20 | 308.625 |
| −17 | 5 | −3 | −2 | −3.4 |
The four steps
OpenStax Prealgebra teaches long division as a repeating cycle: divide, multiply, subtract and bring down. Divide the first part of the dividend by the divisor, multiply the divisor by that digit, subtract the product, then bring down the next digit and repeat until no digits remain. Whatever is left is the remainder. Writing each step under the last one keeps the place values lined up.
A larger example
For 9,876 ÷ 32: 32 goes into 98 three times (96), leaving 2; bring down 7 to make 27. 32 goes into 27 zero times, so write 0 and bring down 6 to make 276. 32 goes into 276 eight times (256), leaving 20. The quotient is 308 R 20, which the long division calculator confirms. Forgetting the zero in the quotient is one of the most common mistakes.
Negative numbers
With a negative dividend the tool divides toward zero and gives the remainder the sign of the dividend, so −17 ÷ 5 is −3 R −2, because 5 × (−3) + (−2) = −17. Some textbooks prefer a positive remainder instead, −4 R 3, which also checks out. Both follow the same check equation.
What to do with the remainder
Word problems decide how to use the remainder. If 125 students ride in vans that hold 4, you need 32 vans, because the extra student still needs a seat: round the quotient up. If you cut 125 cm of ribbon into 4 cm pieces, you get 31 pieces with 1 cm left over: keep the quotient and ignore the rest. If you share $125 among 4 people, each gets $31.25: turn the remainder into a decimal. Reading the question carefully tells you which answer it wants.
You can write the result as a mixed number too. 125 ÷ 4 = 31 1/4, where the remainder becomes the numerator and the divisor becomes the denominator. Simplify the fraction if you can: 1,000 ÷ 8 has a remainder of 0, while 1,002 ÷ 8 = 125 2/8, which simplifies to 125 1/4.
Practice and checking
Estimate first so you can spot errors: 9,876 ÷ 32 should be a little over 300, because 32 × 300 = 9,600. Then work the problem by hand, and use the long division calculator to check the quotient and remainder. Divisibility rules help too: a number is divisible by 3 if its digits add to a multiple of 3, and by 4 if its last two digits form a multiple of 4. A number is divisible by 9 if its digits add to a multiple of 9, and by 5 if it ends in 0 or 5.
Related converters and calculators
Related calculators:
- Fraction calculator: fractions
- Factor calculator: factors
- Percentage calculator: percentages
- LCM calculator: multiples
Sources
OpenStax Prealgebra 2e, 1.5: Divide whole numbers.
Formula and method
Quotient = trunc(dividend ÷ divisor); remainder = dividend − divisor × quotient; decimal shows the repeating block in parentheses.
Whole-number inputs show Q R r, the decimal and mixed number. Decimal inputs return a decimal quotient.
Questions about this calculator
What is 125 divided by 4?
31 remainder 1, or 31.25.
How do I check my answer?
Divisor × quotient + remainder should equal the dividend.
Can I divide by zero?
No, division by zero is undefined.
Does it handle decimals?
Yes, decimal inputs give a decimal quotient.
How do I turn the remainder into a decimal?
Divide the remainder by the divisor.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
Report a calculation issue