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How This Calculator Works
Long division breaks a division problem into a sequence of smaller steps, one digit of the
dividend at a time. Enter a dividend and a divisor to see the quotient, remainder, decimal
result, and the exact step-by-step process — the same “bring down the next digit” method taught
in school.
The Formula
At each step:
Bring down the next digit of the dividend and add it to whatever remainder carried over from
the previous step.
Divide that value by the divisor — the whole-number result is this step’s quotient digit.
Multiply the quotient digit by the divisor and subtract it from the value to find the new
remainder, which carries into the next step.
After processing every digit, the quotient digits collected form the final quotient, and whatever
remainder is left over is the final remainder.
Worked Example
Dividing 984 ÷ 7:
Bring down 9: 9 ÷ 7 = 1 remainder 2.
Bring down 8 (making 28): 28 ÷ 7 = 4 remainder 0.
Bring down 4: 4 ÷ 7 = 0 remainder 4.
Quotient digits: 1, 4, 0 → 140, with a remainder of 4 (984 = 140 × 7 + 4), or
140.571429 as a decimal.
Cómo funciona esta calculadora
La división larga divide un problema de división en una secuencia de pasos más pequeños, un
dígito del dividendo a la vez. Ingresa un dividendo y un divisor para ver el cociente, el
residuo, el resultado decimal y el proceso paso a paso exacto — el mismo método de “bajar el
siguiente dígito” que se enseña en la escuela.
La fórmula
En cada paso:
Baja el siguiente dígito del dividendo y súmalo al residuo que haya quedado del paso anterior.
Divide ese valor entre el divisor — el resultado entero es el dígito del cociente de este paso.
Multiplica el dígito del cociente por el divisor y réstalo del valor para hallar el nuevo
residuo, que se traslada al siguiente paso.
Después de procesar cada dígito, los dígitos del cociente reunidos forman el cociente final, y el
residuo que quede es el residuo final.
Ejemplo resuelto
Dividiendo 984 ÷ 7:
Baja el 9: 9 ÷ 7 = 1 residuo 2.
Baja el 8 (formando 28): 28 ÷ 7 = 4 residuo 0.
Baja el 4: 4 ÷ 7 = 0 residuo 4.
Dígitos del cociente: 1, 4, 0 → 140, con un residuo de 4 (984 = 140 × 7 + 4), o
140.571429 como decimal.
One digit of the dividend at a time: bring down the next digit (adding it to whatever remainder carried over), divide by the divisor to get this step's quotient digit, then multiply and subtract to find the new remainder that carries into the next digit.
What does the remainder mean?
The remainder is whatever is left over after dividing as many whole times as possible — it's always smaller than the divisor. Dividend = Quotient x Divisor + Remainder always holds true, which is a quick way to double-check any long division result.
Can I divide by a number larger than the dividend?
Yes — the quotient will simply be 0, and the remainder will equal the dividend itself, since the divisor doesn't fit into it even once.
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