Long Division Calculator

A long division calculator divides one number by another and returns the quotient, the remainder, the decimal value, and the full step-by-step work. For example, 945 ÷ 5 = 189 with a remainder of 0, while 256 ÷ 3 = 85 remainder 1 (85.333…, with the 3 repeating). Enter any dividend and divisor to see every divide-multiply-subtract-bring-down step laid out.

This tool does more than hand you an answer: it shows 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 (the example it opens with) and you will see the quotient is 689 with a remainder of 0, and how the algorithm gets there one digit at a time. It also handles decimals (12.6 ÷ 0.3 becomes 126 ÷ 3) and can keep dividing past the decimal point until the answer ends or starts to repeat. To turn that decimal into a fraction, use the Decimal to Fraction Calculator; for just the remainder of a division, the Modulo Calculator is the quickest tool.

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.

945 divided by 5 using long division, step by step

Here is the same problem written out as a step table, the same work the calculator generates. Each row is one divide-multiply-subtract-bring-down cycle.

Reading the quotient-digit column top to bottom gives 189, and the final remainder is 0, so 945 ÷ 5 = 189 exactly.

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). Commas, decimals and a minus sign are fine.
2. Enter the divisor, the number you are dividing by (for example 7 or 0.3).
3. Read the result instantly: the large number is the whole-number quotient with its remainder; below it you get the exact decimal (repeating digits under a bar) and the fraction.
4. Follow the steps: the bracket layout shows each product and remainder under the dividend, and the numbered list explains every bring-down, multiplication and subtraction. Tick "Keep dividing past the decimal point" to continue into decimal places.
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, 1003 ÷ 8, 256 ÷ 16, 945 ÷ 5, 10 ÷ 3 and 12.6 ÷ 0.3) to see different cases (exact answers, remainders, repeating decimals and decimal divisors) without typing anything.

The long division steps, in order

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

• 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 (dividing with remainders starts in Grade 4, and fluent multi-digit division is a Grade 6 Common Core standard).
• 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.
• Repeating decimal: a decimal whose digits fall into a block that repeats forever, such as 0.142857142857… for 1 ÷ 7.

Worked example 1: a clean remainder of zero

256 ÷ 16. 16 does not go into 2, so there is no quotient digit yet 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, keep dividing: write a decimal point, bring down a 0 to make 30 (8 goes in 3 times, remainder 6), then 60 (7 times, remainder 4), then 40 (5 times, remainder 0). So 1003 ÷ 8 = 125.375, the same as 3 ÷ 8 = 0.375 added to 125.

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, you bring down a 0 to make 10 again, which gives another 3 and another remainder of 1. Because the remainder repeats, the digit 3 repeats forever: 10 ÷ 3 = 3.333… The calculator detects the repeated remainder and writes the answer as 3.3, with a bar over the repeating digit, instead of rounding it.

Long division answers for popular problems

These are common "X divided by Y" searches solved for you, showing the whole-number quotient, the remainder, and the exact decimal value. Repeating decimals are written with a bar over the digits that repeat.

256 divided by 2 through 12 (quick reference)

Dividing one number by a range of divisors shows how the remainder and decimal shift. Here 256 is divided by every number from 2 to 12, with the remainder also written as a reduced fraction over the divisor ("none" when the division is exact).

Handy reference: list the divisor's multiples first

Writing out the divisor's multiples before you start turns every quotient digit into a lookup instead of a guess. For 4,823 ÷ 7, the list below shows at a glance that 7 fits into 48 six times (42 is the largest multiple not above 48), into 62 eight times (56), and into 63 nine times (63).

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 (like the list 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 after you have started, 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: the Fraction Calculator does the arithmetic for you, while the Decimal to Fraction Calculator runs the conversion the other way. Ratios and proportions often reduce to a division you can run here or simplify with the Ratio Calculator. 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, which the Average Calculator automates.

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. The calculator shows the fraction in lowest terms (256 ÷ 6 = 42 4/6 = 42 2/3), and the Fraction Calculator can simplify any other fraction for you.

Long division vs. short division

Short division is the compact cousin of long division used when the divisor is a single digit (and you are comfortable carrying remainders in your head). Instead of writing out every multiply-and-subtract line, you tuck the carried remainder as a small superscript in front of the next digit. For example, 945 ÷ 5 becomes 9 (1 remainder 4), then a carried 44 (8 remainder 4), then a carried 45 (9 remainder 0): the same answer of 189, just with the scaffolding hidden. Long division is the safer choice for multi-digit divisors and for showing your work, which is why it is the method this calculator displays. Once you trust the steps, short division is a fast shortcut for simple divisors.

Why estimating the first digit matters

The single biggest time-saver in long division is guessing the right quotient digit on the first attempt. If the divisor is 7 and the partial dividend is 48, a quick mental estimate (7 × 7 = 49, just over 48) tells you the digit is 6, not 7, with no trial and error. This is where rounding helps: round the divisor to the nearest ten, divide roughly, and adjust. The same estimation instinct underpins mental math generally, and you can sharpen the rounding half of it with the Rounding Calculator. Strong estimation also lets you sanity-check the final answer: 4,823 ÷ 7 should be "a bit under 700" because 7 × 700 = 4,900, so a quotient of 689 looks right while a quotient of 68 or 6,890 would immediately signal a misplaced digit.

Divisibility shortcuts worth memorizing

Before you start dividing, a few divisibility rules tell you instantly whether the remainder will be zero, and sometimes save the long division entirely:

• Divisible by 2: the last digit is even (0, 2, 4, 6, 8).
• Divisible by 3: the digit sum is a multiple of 3 (for 4,823, 4+8+2+3 = 17, not a multiple of 3, so it leaves a remainder).
• Divisible by 4: the last two digits form a multiple of 4.
• Divisible by 5: the last digit is 0 or 5.
• Divisible by 9: the digit sum is a multiple of 9.
• Divisible by 10: the last digit is 0.

These rules pair naturally with finding common factors. If you are reducing a fraction or hunting for a shared divisor between two numbers, the GCF Calculator finds the greatest common factor directly, and the Prime Factorization Calculator breaks each number into its prime building blocks so you can see every divisor at a glance.

How it compares to related calculators

This page answers "what is the quotient, remainder, and decimal of this division, with the steps shown?" If your question is slightly different, a sister tool fits better:

• To add, subtract, multiply, or divide fractions, use the Fraction Calculator.
• To turn a decimal answer back into a simplified fraction, use the Decimal to Fraction Calculator.
• To simplify or scale a ratio derived from a division, use the Ratio Calculator.
• To average a set of numbers (a sum divided by a count), use the Average Calculator.
• To find shared divisors, use the GCF Calculator or the LCM Calculator.
• To divide a polynomial by a linear factor, use the Synthetic Division Calculator.
• For trig, logs, powers, and mixed expressions, switch to the full Scientific Calculator.

Sources

• Common Core State Standards: 4.NBT.B.6 (whole-number quotients and remainders with one-digit divisors) and 5.NBT.B.6 (two-digit divisors).
• Common Core State Standards: 6.NS.B.2 (fluently divide multi-digit numbers using the standard algorithm) and 7.NS.A.2d (convert a rational number to a decimal using long division; the decimal terminates in 0s or eventually repeats).