Long Division Calculator

Long division is the method for dividing one number by another when the answer is not obvious in your head - and it is the skill behind converting fractions to decimals, splitting amounts into equal shares, and dividing big numbers without a calculator. This long division calculator does more than hand you an answer: it shows the full quotient and remainder, the decimal value, and a clear step-by-step breakdown of every "bring down" so you can follow exactly how the result is built. Enter a dividend like 4,823 and a divisor like 7 and you will see the quotient is 689 with a remainder of 0 - and how the algorithm gets there one digit at a time.

A quick worked example

Take 945 ÷ 5. Working left to right: 5 goes into 9 once (5 × 1 = 5, remainder 4); bring down the 4 to make 44, and 5 goes into 44 eight times (5 × 8 = 40, remainder 4); bring down the 5 to make 45, and 5 goes into 45 nine times exactly (5 × 9 = 45, remainder 0). The digits on top - 1, 8, 9 - form the quotient 189, with a remainder of 0. That is precisely the work the calculator lays out for you.

The long division definition and relationship

Long division splits a dividend by a divisor to produce a quotient and a remainder. The four values are always tied together by one identity:

and the remainder is always smaller than the divisor (0 ≤ remainder < divisor). To get the decimal form instead, you simply continue dividing the remainder: decimal = dividend ÷ divisor. Both forms describe the same result - one as "whole groups plus what is left over," the other as a single number with a fractional part.

How to use this calculator

1. Enter the dividend - the number you want to divide (for example 4823).
2. Enter the divisor - the number you are dividing by (for example 7).
3. Read the result instantly: the large number is the whole-number quotient; below it you get the remainder and the decimal value.
4. Scroll the steps to see each bring-down, multiplication and subtraction, plus the classic stacked long-division layout.
5. Verify with the built-in check, which multiplies the quotient by the divisor and adds the remainder to recover the dividend.

Try the example chips (4823 ÷ 7, 1000 ÷ 8, 256 ÷ 16, 945 ÷ 5) to see different cases - exact answers, remainders and decimals - without typing anything.

The long division steps, in order

Every long-division problem repeats the same five-step cycle until you run out of digits. A common way to remember it is "Does McDonald's Sell Burgers?" - Divide, Multiply, Subtract, Bring down:

• Divide: how many whole times does the divisor fit into the current number? Write that digit on top.
• Multiply: multiply the divisor by that digit.
• Subtract: subtract the product from the current number to find what is left.
• Bring down: drop the next digit of the dividend beside the result.
• Repeat: continue until every digit has been brought down. The final leftover is the remainder.

Who this calculator is for

• Students learning the algorithm who want to see each step modeled correctly.
• Parents and tutors checking homework and explaining where a hand-worked problem went off track.
• Teachers generating clean worked examples for a lesson or worksheet.
• Anyone who needs a quick quotient-and-remainder, or a fraction turned into a decimal, with the working shown.

Key terms explained

• Dividend: the number being divided (it sits inside the division bracket).
• Divisor: the number you divide by (it sits to the left of the bracket).
• Quotient: the answer - how many whole times the divisor fits, written on top.
• Remainder: the amount left over that the divisor cannot divide evenly; always less than the divisor.
• Partial dividend: the running number you are dividing into at each step after bringing a digit down.
• Exact division: a problem with a remainder of 0, meaning the divisor divides the dividend evenly.

Worked example 1: a clean remainder of zero

256 ÷ 16. 16 does not go into 2, so the first quotient digit is 0 and we carry 2. 16 goes into 25 once (16 × 1 = 16, remainder 9); bring down the 6 to make 96, and 16 goes into 96 six times exactly (16 × 6 = 96, remainder 0). The quotient is 16 with a remainder of 0 - an exact division - and the decimal value is simply 16.

Worked example 2: a problem with a remainder

1003 ÷ 8. 8 goes into 10 once (remainder 2); bring down 0 to make 20, and 8 goes in twice (remainder 4); bring down 3 to make 43, and 8 goes in five times (8 × 5 = 40, remainder 3). The quotient is 125 with a remainder of 3. To express that as a decimal, divide the remainder: 3 ÷ 8 = 0.375, so 1003 ÷ 8 = 125.375.

Worked example 3: a repeating decimal

10 ÷ 3. 3 goes into 10 three times (3 × 3 = 9, remainder 1). The quotient is 3 with a remainder of 1. If you keep dividing into the decimals, the digit 3 repeats forever: 10 ÷ 3 = 3.333… This is a repeating decimal; the calculator shows it rounded to 10 places with an ellipsis so you know it does not terminate.

Handy reference: perfect squares

Quick recall of perfect squares makes estimating quotients much faster - if you can spot that the divisor times a number lands near your partial dividend, you can pick the right digit on the first try.

Tips for faster, more accurate long division

• Estimate first: round the divisor and dividend to judge roughly how big the answer should be, so an obviously wrong digit jumps out.
• Keep your columns aligned: write each digit directly above the one you are working on; misaligned columns are the number-one cause of errors.
• Use times tables: knowing the divisor's multiples (and the squares above) means you rarely have to guess how many times it fits.
• Always check: multiply the quotient by the divisor and add the remainder - you should land back on the dividend.
• Do not skip zeros: if the divisor does not fit, write a 0 in the quotient and carry on; dropping that 0 shifts every following digit.

Common pitfalls explained

Most long-division mistakes are mechanical, not conceptual. Forgetting to write a 0 when the divisor does not fit collapses the quotient by a digit. Subtracting incorrectly throws off every later step because the wrong remainder gets carried forward. And stopping too early - before all digits are brought down - leaves you with the wrong remainder. The step view here flags each bring-down explicitly so these slips are easy to catch.

Related concepts

Long division connects to several other math skills. Converting a fraction to a decimal is just long division of the numerator by the denominator. Ratios and proportions often reduce to a division you can run here. The same divide-multiply-subtract-bring-down rhythm reappears later as polynomial long division in algebra. And whenever you compute an average, you are dividing a sum by a count - long division under the hood.

From remainder to fraction

A remainder can also be written as a fraction over the divisor. For 1003 ÷ 8 = 125 remainder 3, the mixed-number form is 125 and 3/8, which equals the decimal 125.375. This is why "quotient with remainder," "mixed number," and "decimal" are three views of the same answer - choose whichever fits the problem you are solving.