Long Division
Step-by-step division
About This Calculator
Long division is a step-by-step method for dividing large numbers by breaking the problem into a sequence of easier division, multiplication, and subtraction steps. It remains a fundamental arithmetic skill and is the basis for polynomial division in algebra. The process produces a quotient and a remainder.
Formula
Dividend ÷ Divisor = Quotient remainder R
Dividend = Divisor × Quotient + Remainder
Check: Divisor × Quotient + R = Dividend
Example Calculation
Divide 847 by 12.
- 12 goes into 84 seven times (12 × 7 = 84), remainder 0
- Bring down 7: 12 goes into 07 zero times, remainder 7
- 847 = 12 × 70 + 7
847 ÷ 12 = 70 remainder 7
Divisibility Rules
| Divisible by | Rule |
|---|---|
| 2 | Last digit is even (0, 2, 4, 6, 8) |
| 3 | Sum of digits is divisible by 3 |
| 4 | Last two digits form a number divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 8 | Last three digits form a number divisible by 8 |
| 9 | Sum of digits is divisible by 9 |
| 10 | Last digit is 0 |
Frequently Asked Questions
What if the remainder is 0?
If the remainder is 0, the divisor divides the dividend evenly. The dividend is said to be divisible by the divisor.
How do I express the remainder as a fraction?
Write the remainder over the divisor. For 847 ÷ 12 = 70 remainder 7, the mixed number form is 70 and 7/12.
What is the difference between the quotient and the remainder?
The quotient is the whole number result of the division. The remainder is what is left over after the divisor has been multiplied by the quotient.