Long Division Calculator

Long division is the process of dividing one number (the dividend) by another (the divisor) to find the quotient and remainder. The quotient is how many times the divisor fits into the dividend; the remainder is what is left over. The decimal result shows the exact value including fractional parts. Long division is a foundational arithmetic skill that extends to polynomial division and other algebraic operations.

This calculator takes a dividend and a divisor and returns the whole-number quotient, the remainder, and the exact decimal value, plus a verification line that confirms the answer reconciles. It is built for primary and middle-school students learning the standard algorithm, for parents checking homework, and for anyone who needs a fast, reliable division with the remainder spelled out rather than hidden inside a decimal. Because the digit-by-digit layout and the remainder check only behave cleanly for whole numbers, this tool works on non-negative integers — decimal inputs are floored before dividing.

Terminology

Dividend ÷ Divisor = Quotient remainder R

Dividend: The number being divided

Divisor: The number you divide by

Quotient: The whole-number result

Remainder: What is left over (0 ≤ R < divisor)

How the Algorithm Works

The classic "long" method works left to right through the dividend, one digit at a time, repeating the same four steps — divide, multiply, subtract, bring down:

• Divide: see how many times the divisor fits into the current leading part of the dividend, and write that digit in the quotient.
• Multiply: multiply that quotient digit by the divisor.
• Subtract: subtract the product from the part you were working on.
• Bring down: bring down the next digit of the dividend and repeat.

When there are no digits left to bring down, whatever is left after the final subtraction is the remainder. To continue into a decimal, place a decimal point in the quotient, append zeros to the dividend, and keep bringing them down.

Worked Example

Divide 17 by 5. Five does not fit into the single digit 1, so look at 17 as a whole: 5 fits into 17 three times because 5 × 3 = 15, which is the largest multiple of 5 that does not exceed 17. Write 3 as the quotient and subtract: 17 − 15 = 2. There are no more digits to bring down, so the remainder is 2. The result is 3 remainder 2, written 17 = 5 × 3 + 2. To express it as a decimal, add a decimal point and a zero to make 20, divide 20 by 5 to get 4 with nothing left over, giving 3.4. Enter 17 and 5 above and the calculator shows the quotient 3, remainder 2, decimal 3.4, and the verification 5 × 3 + 2 = 17.

Checking Your Answer

Every long-division result can be verified with one multiplication and one addition using the identity Dividend = Divisor × Quotient + Remainder. If you multiply the divisor by the quotient and add the remainder, you should land back on the original dividend exactly. This calculator runs that check for you and marks it with a tick when it balances. The remainder must always be smaller than the divisor — if it is equal to or larger, the quotient was too small and you can fit the divisor in at least one more time.

Tips

Estimate first: a rough sense of the answer (for 100 ÷ 7, somewhere in the low teens) catches large errors immediately. Keep your columns neatly aligned so digits line up under the right place value — most beginner mistakes are really alignment mistakes. If the divisor does not go into the leading digit, take in one more digit before writing the first quotient figure, and remember to place a 0 in the quotient whenever the current part is too small to contain the divisor at all.

Common Mistakes

The most common error is forgetting a zero in the quotient when a brought-down value is smaller than the divisor — skipping it shifts every later digit and ruins the answer. Others include subtracting incorrectly, misaligning columns, or stopping with a remainder that is still larger than the divisor. When extending to decimals, do not forget to place the decimal point in the quotient directly above its position in the dividend. And dividing by zero is undefined — there is no number of times that zero "fits" into a non-zero dividend — so the calculator flags it instead of returning a value.