Long Division Calculator
Divide one whole number by another to get the quotient, the remainder and the exact decimal result.
How it works
dividend ÷ divisor = quotient with remainder, where dividend = divisor × quotient + remainder
Long division splits a division into a whole-number quotient and a leftover remainder that is always smaller than the divisor. The identity dividend = divisor × quotient + remainder is the check: multiply the quotient back by the divisor and add the remainder, and you must land on the original dividend. Carrying the division past the decimal point instead of stopping gives the exact decimal result.
Worked example
127 ÷ 4: four goes into 12 three times (12), bring down the 7 to make 7, and four goes into 7 once with 3 left over. So the quotient is 31, the remainder is 3, and 127 = 4 × 31 + 3. As a decimal, 127 ÷ 4 = 31.75.
Sources: Long division — Wikipedia
Frequently asked questions
Why is the remainder always smaller than the divisor?
If the remainder were as large as the divisor, the divisor would fit in one more time, raising the quotient. The leftover is whatever is too small to make another whole group.
How does the remainder become the decimal?
Divide the remainder by the divisor: 3 ÷ 4 = 0.75, which is why 127 ÷ 4 = 31.75. A remainder of 0 means the decimal terminates at the whole number.
What happens with negative numbers?
This calculator truncates toward zero, so the remainder takes the sign of the dividend and dividend = divisor × quotient + remainder still holds. −127 ÷ 4 gives quotient −31 and remainder −3.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.