Long division splits one integer into another and reports two parts: the quotient (how many times the divisor fits) and the remainder (what is left).
About this calculator
Long division splits one integer into another and reports two parts: the quotient (how many times the divisor fits) and the remainder (what is left). The relationship is always dividend = divisor × quotient + remainder. For example, 847 ÷ 13 gives quotient 65 and remainder 2 because 13 × 65 + 2 = 847.
This calculator handles positive and negative integers. Enter the dividend and divisor to see the quotient, remainder, the full equation, and working steps when the division is non-trivial. Exact division shows remainder zero.
Long division is core arithmetic for fractions, ratios, and modular maths. For related work use the [[fraction]] calculator to simplify results, the [[percentage]] calculator for part-of-whole problems, and the [[ratio]] calculator when splitting quantities.
Common uses
- Check school long division homework
- Find quotient and remainder for programming modulo logic
- Verify whether one number divides another evenly
- Break totals into equal groups with leftovers
Frequently asked questions
What is 847 divided by 13?
847 ÷ 13 = 65 remainder 2. Check: 13 × 65 = 845, plus 2 gives 847. The quotient is 65 and the remainder is 2.
What is the difference between quotient and remainder?
The quotient is how many whole times the divisor fits into the dividend. The remainder is the amount left after those full groups are removed.
Can the remainder be larger than the divisor?
In standard division with integers, the remainder is always less than the divisor in absolute value. If it were larger, you could take one more group from the dividend.
What happens when you divide by zero?
Division by zero is undefined. The calculator asks for a non-zero divisor because no integer quotient satisfies a ÷ 0.