Long Division Calculator
Educational tool that generates step-by-step long division worksheets. Visualizes the divide, multiply, subtract, bring-down process.
About
Long division is an algorithmic procedure for dividing simple or complex multidigit numbers. It breaks down a division problem into a series of easier steps. This helps students visualize the magnitude of the quotient and the derivation of the remainder.
This tool automates the manual process taught in classrooms. It generates the complete "work" required to solve the equation rather than just the final answer. It strictly follows the standard DMSB process:
- ÷ Divide: Determine how many times the divisor fits into the current digits.
- × Multiply: Multiply the partial quotient by the divisor.
- − Subtract: Find the difference.
- ↓ Bring Down: Drop the next digit of the dividend to continue.
Visualizing these steps allows for easier debugging of arithmetic errors in homework or test preparation. The calculator supports remainders and handles zero placeholders correctly.
Formulas
The long division algorithm iterates through the digits of the dividend A from left to right. For each step i, we seek a digit d such that:
Where B is the divisor and Ri is the current working value (remainder from previous step concatenated with the next digit). This process repeats until all digits of A are exhausted leaving a final remainder r.
Reference Data
| Divisor | Divisibility Rule | Example Check (x = 144) |
|---|---|---|
| 2 | Last digit is even (0, 2, 4, 6, 8) | 4 is even &implies; Yes |
| 3 | Sum of digits is divisible by 3 | 1+4+4=9. 9÷3=3 &implies; Yes |
| 4 | Last two digits are divisible by 4 | 44÷4=11 &implies; Yes |
| 5 | Last digit is 0 or 5 | Last is 4 &implies; No |
| 6 | Divisible by BOTH 2 and 3 | Yes and Yes &implies; Yes |
| 8 | Last three digits divisible by 8 | 144÷8=18 &implies; Yes |
| 9 | Sum of digits is divisible by 9 | 1+4+4=9 &implies; Yes |
| 10 | Last digit is 0 | Last is 4 &implies; No |