β Long Division Calculator
Every step shown: divide, multiply, subtract, bring down.
Quotient
How to Use the Long Division Calculator
Enter the dividend (the number being divided) and the divisor (the number dividing it). You will get the quotient, remainder, decimal answer, and a step-by-step walkthrough of the classic long division algorithm.
Enter the dividend and divisor as whole numbers.
Read the quotient and remainder, plus the decimal expansion.
Follow the step list to see each divide, multiply, subtract, and bring-down cycle.
The Long Division Algorithm
Long division processes the dividend left to right, one digit at a time. At each stage you ask: how many times does the divisor go into the current partial number? That digit goes on top in the quotient. Multiply it back by the divisor, subtract, and bring down the next digit. Repeat until every digit is used. Whatever is left at the bottom is the remainder. The worked example for 947 Γ· 7: 7 goes into 9 once (1Γ7=7, 9β7=2), bring down 4 to make 24; 7 goes into 24 three times (3Γ7=21, 24β21=3), bring down 7 to make 37; 7 goes into 37 five times (5Γ7=35, 37β35=2). Quotient 135, remainder 2.
Remainder vs Decimal Answers
Remainder form (135 R 2) answers "how many whole groups and what is left over," which fits sharing problems and integer homework. Decimal form (135.285714...) answers "exactly how much per group," which fits money, measurement, and science. To convert, divide the remainder by the divisor: 2/7 β 0.2857, so 135 + 0.2857 = 135.2857. Some divisions never terminate (1/3 = 0.333...) or repeat; the calculator shows 10 decimal places.
Checking Your Work
The universal check: (quotient Γ divisor) + remainder = dividend. Apply it to every problem before moving on. Most long division errors come from multiplication slips (6Γ7=42, not 48) or subtraction errors in the middle steps, so verify those two lines first when the check fails. Estimation also helps: 947 Γ· 7 is roughly 1000 Γ· 7 β 143, so an answer of 135 is plausible but 1,350 is not.
Frequently Asked Questions
What are the steps of long division?
The classic cycle is: Divide, Multiply, Subtract, Bring down, Repeat. Divide the current partial dividend by the divisor, multiply the quotient digit back, subtract from the partial dividend, bring down the next digit, and repeat until no digits remain. The calculator animates each cycle so you can follow along.
How do I write the answer: decimal or remainder?
Both are valid and this tool shows both. Use remainder form (e.g. 47 R 3) for integer division problems and elementary homework. Use decimal form (47.428...) for measurements, money, and science. The decimal here shows up to 10 places.
What is the difference between long division and short division?
Short division does the same math but keeps the subtraction mental, writing only small carried numbers. It works well for single-digit divisors. Long division writes every step, which is better for multi-digit divisors and for learning, because every step is visible and checkable.
How do I check my division answer?
Multiply the quotient by the divisor and add the remainder: you must get the dividend back. Example: 947 Γ· 7 = 135 R 2, check: 135 Γ 7 + 2 = 947. If it does not match, re-check the multiply and subtract steps; errors hide there most often.
Why do we bring down digits one at a time?
Each bring-down extends the partial dividend by one place value, letting you divide the next smaller chunk. It mirrors how the dividend is built from hundreds, tens, and ones. If the partial dividend is still smaller than the divisor after bringing down, you write 0 in the quotient and bring down another digit.