How long division works
Long division finds how many whole times a divisor fits into a dividend, plus what is left over. For 17 ÷ 5, five fits into 17 three times (5 × 3 = 15) with 2 left over, so the quotient is 3 and the remainder is 2.
Done by hand the method works one digit at a time from the left. You ask how many times the divisor fits into the leading part of the dividend, write that digit above, subtract, then bring down the next digit and repeat. The process stops when no digits remain, and whatever is left at the bottom is the remainder. If all you need is the leftover rather than the full quotient, the modulo calculator returns the remainder directly.
How to use this calculator
Enter the dividend (the number being divided) and the divisor (the number you divide by). The divisor cannot be zero. The result shows the whole-number quotient and the remainder. To round a decimal answer instead, use the rounding calculator.
Order matters: 17 ÷ 5 and 5 ÷ 17 are entirely different sums, so if the quotient comes back as 0 the two entries are probably the wrong way round.
Quotient, remainder and the original number
The relationship is dividend = divisor × quotient + remainder. You can always check the answer this way: 5 × 3 + 2 = 17. The remainder is always smaller than the divisor.
If it were not, the divisor would fit at least once more. A remainder of exactly 0 means the division is exact and the divisor is a factor of the dividend — the same test used for divisibility. Carrying the division past the decimal point is exactly what the fraction to decimal calculator does.
Frequently asked questions
- What is 17 divided by 5?
- The quotient is 3 with a remainder of 2, because 5 × 3 = 15 and 17 − 15 = 2.
- What is the difference between quotient and remainder?
- The quotient is how many whole times the divisor fits; the remainder is what is left over after that.
- Can the divisor be zero?
- No. Dividing by zero is undefined, so the calculator requires a non-zero divisor.
- How can I check a long division answer?
- Multiply the divisor by the quotient and add the remainder — you should get the original dividend.
- How do I turn the remainder into a decimal or a fraction?
- Divide the remainder by the divisor. For 17 ÷ 5 the remainder 2 over the divisor 5 gives 0.4, so the full answer is 3.4, or 3 and 2/5 written as a mixed number.