Enter a dividend and a divisor to perform long division step by step. The Long Division Calculator returns the quotient, remainder, and decimal result — plus a full breakdown of each division step so you can follow the working clearly.
Quotient
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Remainder
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Decimal Quotient
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Division Statement
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Long division is a systematic method for dividing large numbers by breaking the problem into a sequence of simpler steps — divide, multiply, subtract, and bring down. It is also known as the bus stop or standard algorithm method and works for any size of dividend and divisor.
A long division problem has four key parts: the <strong>dividend</strong> (the number being divided), the <strong>divisor</strong> (the number you divide by), the <strong>quotient</strong> (the whole-number result), and the <strong>remainder</strong> (what is left over after division). For example, in 487 ÷ 32 = 15 R 7, the dividend is 487, divisor is 32, quotient is 15, and remainder is 7.
Work through the dividend digit by digit from left to right. At each step: (1) determine how many times the divisor fits into the current partial dividend, (2) write that digit as part of the quotient, (3) multiply it by the divisor and subtract from the partial dividend, then (4) bring down the next digit and repeat. Whatever is left when no digits remain is the remainder.
The decimal quotient is simply the dividend divided by the divisor using standard division (e.g. 487 ÷ 32 = 15.21875). It represents the exact value without stopping at a whole-number remainder, and can be continued to as many decimal places as needed.
The remainder is the whole-number leftover after dividing as far as possible without going into decimals. The decimal quotient continues the division past the decimal point to give a precise fractional answer. Both representations are valid — which you use depends on the context of the problem.
Yes. When the divisor is larger than the dividend, the quotient is 0 and the remainder equals the dividend. For example, 5 ÷ 12 gives a quotient of 0, a remainder of 5, and a decimal quotient of approximately 0.4167.
Long division builds number sense and lays the foundation for understanding fractions, decimals, and algebra. It is also practical when a calculator is unavailable and helps students understand why division works, not just how to press a button.
Yes. The step-by-step table below the results shows each division step including the partial dividend used, how many times the divisor fits, the subtracted value, and the running remainder — so you can follow or check the full working of the long division problem.