Long Division Calculator
Perform long division and find the quotient, remainder, and decimal result for any dividend and divisor.
Quotient
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Remainder —
Decimal Result —
Expression —
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Quotient
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Remainder —
Decimal —
Long Division Statement —
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Division Results
Quotient —
Remainder —
Decimal Result —
As Fraction (simplified) —
Analysis
Remainder as % of Divisor —
Verify: Q×D + R = Dividend —
How to Use This Calculator
Enter the Dividend (the number to divide) and the Divisor (what to divide by). The calculator shows the quotient, remainder, and decimal result.
Formula
Dividend = Divisor × Quotient + Remainder • Decimal = Dividend / Divisor
Example
137 ÷ 5 = 27 remainder 2 (decimal: 27.4)
Frequently Asked Questions
- Long division is a step-by-step algorithm for dividing one number (the dividend) by another (the divisor) to produce a quotient and a remainder. The process works by repeatedly estimating how many times the divisor fits into successive portions of the dividend. For example, to divide 137 by 5: 5 goes into 13 twice (2×5=10), remainder 3; bring down 7 to get 37; 5 goes into 37 seven times (7×5=35), remainder 2. Result: quotient = 27, remainder = 2.
- The remainder is what is left over after the dividend has been divided as evenly as possible by the divisor. It is always less than the divisor. Example: 137 ÷ 5 = 27 remainder 2, because 5 × 27 = 135 and 137 − 135 = 2. The relationship is always: Dividend = Divisor × Quotient + Remainder. Remainders are the basis for modular arithmetic (e.g., "137 mod 5 = 2") and are used in hash functions, cyclic patterns, and computing repeating decimals.
- The decimal result equals the quotient plus the remainder divided by the divisor: Decimal = Quotient + Remainder / Divisor. For 137 ÷ 5: Decimal = 27 + 2/5 = 27 + 0.4 = 27.4. For 100 ÷ 3: Quotient = 33, Remainder = 1, Decimal = 33 + 1/3 = 33.333… (repeating). Knowing the remainder tells you the exact fractional part without rounding. This is important in contexts where exact division is needed, such as distributing items evenly.
- The calculator is designed for positive integers. For negative numbers, compute the division using absolute values and then apply sign rules manually: a positive divided by a negative gives a negative quotient, and a negative divided by a negative gives a positive quotient. For example, −137 ÷ 5: compute 137 ÷ 5 = 27 remainder 2, then apply the negative sign → quotient = −27, but note that remainder conventions vary: in math, the remainder is always non-negative, while in programming languages it can take the dividend's sign.
- Division by zero is mathematically undefined — there is no number that, when multiplied by 0, gives a non-zero dividend. Conceptually, dividing 10 by smaller and smaller numbers gives larger and larger results (10/0.1=100, 10/0.01=1000, …), suggesting the result approaches infinity, but infinity is not a real number and division by exactly zero has no defined value. The calculator will display an error message if you enter 0 as the divisor. Always check your divisor before calculating.