The long division calculator performs integer division with a detailed step-by-step solution. Shows every divide, multiply, subtract, and bring-down step, plus the quotient, remainder, fraction, and decimal result.
Long Division Calculator
Step-by-Step Solution
How to Use the Long Division Calculator
The long division calculator breaks down any integer division into individual steps, showing exactly how each digit of the quotient is computed.
Long Division Algorithm
Example: 854 ÷ 7. Step 1: Take 8 (first digit). 8 ÷ 7 = 1, write 1. 1 × 7 = 7. Subtract: 8 − 7 = 1. Step 2: Bring down 5, get 15. 15 ÷ 7 = 2. 2 × 7 = 14. Subtract: 15 − 14 = 1. Step 3: Bring down 4, get 14. 14 ÷ 7 = 2. 2 × 7 = 14. Subtract: 14 − 14 = 0. Result: 854 ÷ 7 = 122 remainder 0.
Interpreting the Remainder
A remainder can be expressed three ways: 47 ÷ 5 = 9 R 2 (remainder notation), 9 2/5 (mixed fraction), or 9.4 (decimal, by continuing division). The decimal form keeps dividing by adding zeros: 20 ÷ 5 = 4, so 47 ÷ 5 = 9.4.
Negative Number Division
Sign rules: positive ÷ positive = positive, negative ÷ negative = positive, mixed signs = negative. The remainder carries the sign of the dividend. 17 ÷ (−3) = −5 R 2 because −5 × (−3) = 15 and 17 − 15 = 2. Check: (−5) × (−3) + 2 = 15 + 2 = 17. ✓
When to Use Long Division
Long division is essential for understanding why division works, polynomial division in algebra, and finding decimal expansions manually. 100 ÷ 3 shows why 0.333... is repeating: after each step you get remainder 1, which becomes 10 again forever. The calculator displays up to 8 decimal places.
FAQ
How do you do long division?
Long division algorithm: (1) Divide the first digit(s) of dividend by divisor. (2) Write the quotient digit. (3) Multiply quotient digit by divisor. (4) Subtract. (5) Bring down the next digit. (6) Repeat until done. Example: 854 ÷ 7: 8÷7=1 r1, bring 5 → 15÷7=2 r1, bring 4 → 14÷7=2. Result: 122.
How do you express the remainder?
Three ways: as remainder (47 ÷ 5 = 9 R 2), as fraction (47 ÷ 5 = 9 2/5), or as decimal (47 ÷ 5 = 9.4). Continue dividing into the decimal places: bring down a zero, 20÷5=4, result 9.4. The calculator shows all three forms.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
Can I divide negative numbers?
Yes. The sign of the quotient: positive/positive=positive, negative/negative=positive, positive/negative=negative. The remainder has the same sign as the dividend. 17 ÷ (−3) = −5 remainder 2 (since −5 × −3 = 15, and 17 − 15 = 2).