Long Division Calculator
Divide two numbers and get the answer as a quotient with a remainder, along with the long division bracket that produced it. Enter the dividend, enter the divisor, and the working appears one subtraction at a time — with decimals to 20 places when you want them.
- Every subtraction shown
- Repeating decimals detected
Long Division Worker
LiveQuotient, remainder and every equivalent form.
- Quotient
- —
- Remainder
- —
The long division, step by step
The bracket below is the same one you would write on paper. It redraws as you type, so changing the divisor shows immediately which subtraction changes with it.
The long division bracket
Quotient on top, dividend under the bar, and each pair of rows is one subtraction followed by the next digit brought down.
Narrated steps
What Is Long Division?
Long division is a written method for dividing one number by another using 4 repeating moves: divide, multiply, subtract, bring down. The method breaks a division that is too large to do in one step into a sequence of small divisions, one per digit of the dividend, and records each one under a bracket so the arithmetic stays aligned.
Long division has 4 named parts. The dividend is the number being divided, the divisor is the number dividing it, the quotient is how many whole times the divisor fits, and the remainder is what is left over. Written as a division sentence, 487 ÷ 32 = 15 R 7 puts 487 as the dividend, 32 as the divisor, 15 as the quotient part of the answer, and 7 as the remainder part of the answer.
Long division with remainders is 1 of 2 ways to finish the method. The first stops at whole numbers and reports what could not be shared out, which is what 15 R 7 records. The second carries on past the decimal point until the remainder reaches zero or a digit pattern repeats, which turns the same division into 15.21875. The decimal places control above switches between the two.
The long division algorithm appears in the Common Core State Standards twice: at grade 4 for dividing by 1-digit divisors (4.NBT.B.6) and at grade 6 for fluency with multi-digit divisors (6.NS.B.2). The same algorithm scales without change from a 2-digit dividend to a 40-digit one, which is what keeps it worth learning after the arithmetic itself stops being the point.
How to Use the Long Division Calculator
To use the long division calculator, enter the dividend, enter the divisor, and read the quotient and remainder. The full working appears below the answer in 4 steps:
- Type the dividend into the first field. The dividend is the number you're dividing, and it accepts up to 40 digits.
- Type the divisor into the second field. The divisor is the number you're dividing by, and 2-digit and 3-digit divisors work the same way as single digits.
- Set the decimal places to 0 for a remainder, or to any value up to 20 for long division with decimals.
- Read the bracket in the working panel. Each pair of rows is one subtraction followed by the next digit brought down.
The calculator handles 5 input cases that trip up other tools. Negative numbers are divided by magnitude with the sign applied to the quotient. Exact divisions report R 0 rather than a blank. Repeating decimals are detected and the repeating block is named. Dividends longer than the double-precision limit stay exact, since the arithmetic runs in arbitrary-precision integers. Division by zero returns an explanation instead of an error code.
How to Do Long Division With Remainders
To do long division with remainders, set the problem up under a division bracket and repeat 4 moves until every digit of the dividend has been used. Dividing 487 by 32 takes 2 rounds of those moves and ends at a quotient of 15 with a remainder of 7.
Start by writing the dividend inside the bracket and the divisor outside it:
32 ) 487
The first digit of the dividend, 4, is smaller than the divisor 32, so the first quotient digit is 0 and the calculation moves on to the first 2 digits, 48. Skipping straight to 48 is the shortcut experienced dividers use; writing the 0 first is the version taught in school. Both reach the same answer.
Step 1: Divide
Divide the current number by the divisor and write the whole-number answer on top of the division bar. 48 ÷ 32 = 1, so the 1 goes above the 8 — directly over the last digit used.
1
───
32 ) 487 Step 2: Multiply
Multiply the quotient digit by the divisor and write the answer under the digits it came from. 1 × 32 = 32, so 32 is written under the 48.
1
───
32 ) 487
-32 Step 3: Subtract
Draw a line and subtract. 48 − 32 = 16, and the 16 goes under the line. The difference is always smaller than the divisor when the quotient digit is right — 16 is smaller than 32, so the digit 1 was correct.
1
───
32 ) 487
-32
───
16 Step 4: Bring Down
Bring down the next number of the dividend and write it beside the difference. The 7 comes down next to the 16, making 167.
1
───
32 ) 487
-32
───
167 Step 5: Repeat Until Finished
Repeat the 4 moves on the new number until no digits are left to bring down. 167 ÷ 32 = 5, then 5 × 32 = 160, then 167 − 160 = 7. Nothing remains to bring down and 7 is smaller than 32, so the long division is finished.
15
───
32 ) 487
-32
───
167
-160
────
7 The quotient is 15 and the remainder is 7, so 487 ÷ 32 = 15 with a remainder of 7. Longer dividends repeat the same 4 moves once more per extra digit, and a 40-digit dividend needs no new rule — only more rows.
Long Division Formula
The long division formula is dividend = divisor × quotient + remainder, with the remainder held below the divisor. Every completed long division satisfies both halves of that statement.
dividend = divisor × quotient + remainder 487 = 32 × 15 + 7 487 = 480 + 7 487 = 487 ✓ with 0 ≤ remainder < divisor 0 ≤ 7 < 32 ✓The second line is what makes the answer unique. Dropping it would let 487 ÷ 32 be written as 14 R 39 or 13 R 71, both of which satisfy the first line. Holding the remainder below the divisor leaves exactly 1 valid pair of answers, which is why the division algorithm is stated with both conditions rather than one.
Rearranging the formula gives the decimal form. Dividing through by the divisor turns 487 = 32 × 15 + 7 into 487/32 = 15 + 7/32, and 7 ÷ 32 = 0.21875, so 487 ÷ 32 = 15.21875. The remainder and the decimal are the same quantity written 2 ways.
The same 4 moves drive several other divisions that carry the long division name:
- Long division with decimals appends zeros to the dividend and continues past the decimal point. 1 ÷ 7 never terminates and repeats the 6-digit block 142857.
- Polynomial long division divides x³ − 6x² + 11x − 6 by x − 3 using the same divide, multiply, subtract, bring down cycle on terms rather than digits. The polynomial remainder theorem calculator handles that case, including synthetic division as the shorter form.
- Binary long division runs the identical algorithm in base 2, where each quotient digit is 0 or 1 and the multiplication step disappears.
- Fraction division reaches the same answer by inverting the divisor and multiplying, which skips the bracket entirely.
- The square root algorithm borrows the bracket layout and works in digit pairs, which is why it is often taught straight after long division.
Mistakes This Calculator Catches
There are 5 common long division mistakes, and 4 of them are caught by checking the answer against the formula.
1. Skipping a zero in the quotient
Write the 0 and bring down the next digit, when the divisor does not fit into the current number. Dropping the 0 shifts every later digit one place left and multiplies the answer by 10.
34 7 ) 2107
301 7 ) 2107
2. Leaving a difference larger than the divisor
Raise the quotient digit by 1 and subtract again, when the difference comes out equal to or larger than the divisor. A difference of 35 after dividing by 32 means another 32 still fits.
32 ) 487
-32
───
35 ← 35 ≥ 32 32 ) 487
-32
───
16 ← 16 < 32 3. Misaligning the columns
Line each product up under the digits it came from. A product written 1 column off changes its place value by a factor of 10 and corrupts every row underneath it. The drawn bracket in the working panel keeps the alignment fixed, which is most of the reason it is worth drawing at all.
4. Forgetting the last digit
Bring down every digit of the dividend before stopping. Finishing at 16 instead of 167 in the example above returns a quotient of 1 rather than 15 — an answer 15 times too small. The check catches it immediately: 1 × 32 + 16 = 48, not 487.
5. Reporting a remainder that is too big
Keep the remainder below the divisor. A written answer of 14 R 39 for 487 ÷ 32 satisfies dividend = divisor × quotient + remainder, and it is still wrong, since 39 is larger than 32. Dividing by 32 produces a remainder between 0 and 31.
Check any long division answer in 2 multiplications: multiply the quotient by the divisor, add the remainder, and compare the total to the dividend. For 487 ÷ 32 = 15 R 7, the check reads 15 × 32 + 7 = 487. The remainder calculator runs the same check in one step, and the divisibility rule checker predicts whether a division will come out exact before the bracket is drawn.