Long Division Calculator: Step-by-Step with Remainder or Decimal
Free long division calculator: quotient with remainder or decimal result. How to do long division with remainders, long division steps for kids, division with decimals. Dividend divisor quotient remainder explained.
What This Calculator Does & Who It's For
Calculator Purpose & Ideal Users
- What You'll Get:Quotient and remainder: e.g. 127 รท 5 = 25 R 2. Decimal result: Optional, with configurable decimal places. Show your work: Each step with annotations (e.g. "5 goes into 12 2 times; 2 ร 5 = 10") and a clear dividend รท divisor summary. Validation: Non-negative integers; divisor must be > 0.
- Scope & Limits:Non-negative integers only. Divisor must be greater than zero. Results and steps within JavaScript safe integer range.
This long division calculator gives step-by-step long division: it performs division and shows every step of the standard algorithm (divide, multiply, subtract, bring down). You get either a quotient with remainder or a decimal result to a chosen number of decimal places.
Components of Division: Dividend, Divisor, Quotient, Remainder Explained
Dividend, divisor, quotient, and remainder explained: In division, the dividend is the number being divided; the divisor is the number that divides it. The quotient is the result (how many times the divisor fits), and the remainder is what is left over. So dividend รท divisor = quotient with remainder, or dividend = divisor ร quotient + remainder. For example, 127 รท 5 = 25 R 2 means 127 = 5 ร 25 + 2. The remainder is always less than the divisor. Every long division calculator uses this breakdown; for "What is the number being divided called?" and "What is a remainder?", see the FAQ above.
How to Perform Long Division Manually
To perform long division (the standard "bus stop" method): (1) Divideโtake the leftmost digits of the dividend that are at least the divisor; see how many times the divisor fits (that is your first quotient digit). (2) Multiplyโmultiply that quotient digit by the divisor. (3) Subtractโsubtract that product from the current portion. (4) Bring downโbring down the next digit of the dividend and repeat. When you run out of digits, what is left is the remainder. These are the long division steps for kids and adults alike; many curricula teach them as DMSB (Divide, Multiply, Subtract, Bring down). For a decimal result, add a decimal point and bring down zeros. This long division calculator shows these steps for any dividend and divisor; the "Show your work" section annotates each step (e.g. "7 goes into 30 four times; 4 ร 7 = 28").
Long Division with Remainders
Long division with remainders stops when you have used all digits of the dividend and the last difference is less than the divisorโthat difference is the remainder. For example, 100 รท 7 = 14 R 2. To turn a remainder into a decimal, continue by writing a decimal point and bringing down zeros; the calculator's "Decimal result" mode does this and shows the steps. For "How do you turn a remainder into a decimal?" see the FAQ above.
Division with Decimals
For a division with decimals result, use the same long division algorithm: after processing all digits of the dividend, add a decimal point in the quotient and "bring down" zeros. Each zero gives another decimal place. For example, 1 รท 2: 2 goes into 10 five times (0.5). A division with decimals calculator like this one lets you set the number of decimal places and see every step; select "Decimal result" and choose your precision to get a decimal quotient.
Long Division Calculator FAQ
What is the number being divided called?
The number being divided is called the dividend. The number that divides it is the divisor. The result is the quotient, and any amount left over is the remainder. So in 127 รท 5 = 25 R 2, 127 is the dividend, 5 is the divisor, 25 is the quotient, and 2 is the remainder.
What is a remainder?
The remainder is what is left after dividing the dividend by the divisor as many whole times as possible. So 127 รท 5 = 25 with remainder 2 because 5 ร 25 = 125 and 127 โ 125 = 2. The remainder is always less than the divisor. Choose "Quotient with remainder" in the calculator to see the remainder; choose "Decimal result" to continue the division and get a decimal answer.
How do you turn a remainder into a decimal?
To turn a remainder into a decimal, continue the long division by adding a decimal point and "bringing down" zeros. For example, 127 รท 5 = 25 R 2; then 2 with a zero brought down gives 20, 5 goes into 20 four times (0.4), so 127 รท 5 = 25.4. Select "Decimal result" in this calculator and set the number of decimal places to see the steps of adding zeros and getting the decimal answer.
How do you do long division with remainders?
Use the standard long division steps: Divide (how many times the divisor fits into the current portion), Multiply (quotient digit ร divisor), Subtract, then Bring down the next digit. Repeat until you run out of digits. What is left is the remainder. This calculator shows each step with annotations (e.g. "5 goes into 12 2 times; 2 ร 5 = 10"). Select "Quotient with remainder" to see the remainder.
What are the long division steps for kids?
The long division steps are often taught as: (1) Divideโsee how many times the divisor fits into the first digit(s); (2) Multiplyโmultiply that number by the divisor; (3) Subtractโtake that product away from the current number; (4) Bring downโbring down the next digit and repeat. This is the "bus stop" or bracket method. The calculator's "Show your work" section displays these long division steps for any dividend and divisor.