Long Division Calculator with Remainders and Steps
Divide whole numbers of up to 30 digits with long division. See the quotient, remainder, mixed number, repeating decimal and the full step-by-step layout, exact and free in your browser.
Result
- Quotient
- 176
- Remainder
- 2
- Mixed number
- 176 2/7
- Check
- 7 × 176 + 2 = 1234
Decimal
176.(285714 repeating)
The digits under the line repeat forever. As text: 176.(285714)
Long division
- 12 ÷ 7 = 1, 1 × 7 = 7, 12 − 7 = 5, bring down 3
- 53 ÷ 7 = 7, 7 × 7 = 49, 53 − 49 = 4, bring down 4
- 44 ÷ 7 = 6, 6 × 7 = 42, 44 − 42 = 2
Long Division Calculator
Enter a dividend and a divisor, both whole numbers of up to 30 digits, and this calculator does the long division for you. It gives the quotient and the remainder, the answer as a mixed number in lowest terms, a check line, and the decimal with any repeating digits marked. Below the answer it draws the long division the way it is written in school and lists each step in words. Every digit is exact, even for 30-digit numbers. The page opens with 1234 ÷ 7.
How long division works
Divide, multiply, subtract, bring down
- Take the shortest leading part of the dividend that the divisor fits into. For 1234 ÷ 7 that is 12.
- Divide: 7 fits into 12 once. Write 1 in the quotient.
- Multiply: 1 × 7 = 7. Subtract: 12 − 7 = 5.
- Bring down the next digit, 3, to make 53, and repeat: 53 ÷ 7 = 7, 7 × 7 = 49, 53 − 49 = 4.
- Bring down 4 to make 44: 44 ÷ 7 = 6, 6 × 7 = 42, 44 − 42 = 2. No digits are left, so the remainder is 2.
The answer is 176 remainder 2, and the check 7 × 176 + 2 = 1234 confirms it.
Remainders, mixed numbers and decimals
The remainder over the divisor is the fraction left over, so 1234 ÷ 7 = 176 2/7. The calculator reduces that fraction, so 10 ÷ 4 = 2 2/4 = 2 1/2. To get the decimal, it keeps dividing past the decimal point, bringing down zeros. When a remainder comes back that it has seen before, the digits from then on repeat forever. That cycle is drawn with a line over it on screen and written in brackets in copied text: 22 ÷ 7 = 3.(142857), 1 ÷ 3 = 0.(3) and 1 ÷ 6 = 0.1(6).
Worked examples
5 ÷ 8
8 does not fit into 5, so the quotient is 0 and the remainder 5. As a decimal, 50 ÷ 8 = 6 r 2, 20 ÷ 8 = 2 r 4 and 40 ÷ 8 = 5 r 0, so 5 ÷ 8 = 0.625 exactly.
987654321 ÷ 123
The quotient is 8,029,709 and the remainder 114, because 123 × 8,029,709 + 114 = 987,654,321.
Long cycles
Some fractions take a long time to repeat. 1 ÷ 97 has a cycle of 96 digits, so the calculator shows the first 50 decimal places, cut rather than rounded, and says that the decimal goes on.
Limits
Both numbers must be whole numbers from 0 upwards with at most 30 digits, and the divisor must be at least 1, because dividing by zero has no answer. To divide decimals, first multiply both numbers by the same power of 10.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
Use the Fraction Calculator to keep working with the remainder as a fraction, the Scientific Calculator for decimal division, and the Percentage Calculator to turn a quotient into a percentage.
Frequently asked questions
How does long division work?
Take the shortest leading part of the dividend that the divisor fits into, write how many times it fits, multiply, subtract, and bring down the next digit. Repeat until every digit is used. What is left is the remainder. For 1234 ÷ 7 the steps are 12 ÷ 7, 53 ÷ 7 and 44 ÷ 7, giving 176 remainder 2.
How do I check a long division answer?
Multiply the divisor by the quotient and add the remainder; you should get the dividend back. For 1234 ÷ 7 the check is 7 × 176 + 2 = 1234.
What does the bracket or line over a decimal mean?
It marks the digits that repeat forever. 1 ÷ 3 = 0.333… is written 0.(3), and 1234 ÷ 7 = 176.(285714). On screen the repeating digits have a line over them; copied text uses brackets.
Why does the decimal stop after 50 places?
Some divisions have very long cycles. 1 ÷ 97 repeats only after 96 digits, so the page shows the first 50, cut rather than rounded, and says that the decimal goes on.
How large can the numbers be?
Both can have up to 30 digits. The calculator uses exact big-integer arithmetic, so a 30-digit dividend gives an exact quotient with every digit, such as 17,636,684,144,620,811,271,604,938,270 for 123456789012345678901234567890 ÷ 7.
Can I divide decimals or negative numbers?
No. The dividend and the divisor must be whole numbers, 0 or greater, and the divisor must be at least 1. To divide decimals, multiply both numbers by the same power of 10 first: 12.5 ÷ 0.5 is the same as 125 ÷ 5.