Long Division Calculator Online Free
Long Division Calculator
Long Division Calculator
The number being divided
The number to divide by
The long division calculator performs division and shows every step of the process, making it ideal for checking homework or learning the algorithm. Enter the dividend and divisor to see the complete worked solution, including quotient, remainder, and optional decimal expansion.
Long Division Steps
Long division breaks a complex division problem into a series of simpler steps: Divide, Multiply, Subtract, Bring down. Repeat until complete.
Divide 847 ÷ 7: 1. 7 goes into 8 once → write 1, subtract: 8-7=1 2. Bring down 4 → 14. 7 goes into 14 twice → write 2, subtract: 14-14=0 3. Bring down 7 → 7. 7 goes into 7 once → write 1, subtract: 7-7=0 847 ÷ 7 = 121 (remainder 0)
Division with Decimals
When the division does not come out evenly, continue after a decimal point. Add zeros to the dividend and continue dividing until the desired precision or the pattern repeats (indicating a repeating decimal).
1 ÷ 3: 1.000 ÷ 3 10 ÷ 3 = 3 r1 10 ÷ 3 = 3 r1 (repeats) 1/3 = 0.333... = 0.3̄
Frequently Asked Questions
What do I do when the divisor is larger than the dividend?⌄
The quotient will be 0 with the whole dividend as remainder (for integer division). For decimal division, place a decimal point after the dividend and add zeros, then divide as normal. 3 ÷ 7 = 0.428571... (3/7 expressed as a decimal).
How do I check my long division answer?⌄
Multiply the quotient by the divisor, then add the remainder. The result should equal the original dividend. If 847 ÷ 7 = 121 remainder 0: check: 121 × 7 + 0 = 847. Correct.
What is the difference between quotient and remainder?⌄
The quotient is the whole number result of the division. The remainder is what is left over after dividing into whole groups. 17 ÷ 5 = 3 remainder 2 (quotient 3, remainder 2). This can also be expressed as 3 and 2/5, or as a decimal 3.4.
How is long division used in polynomial arithmetic?⌄
Polynomial long division divides one polynomial by another using the same algorithm as numeric long division. It is used to factor polynomials, simplify rational expressions, and find roots. For example, dividing (x² + 5x + 6) by (x + 2) gives (x + 3) because (x+2)(x+3) = x² + 5x + 6.