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Divide Calculator

Division Formula:

\[ \text{Quotient} = \left\lfloor\frac{a}{b}\right\rfloor \quad \text{Remainder} = a \bmod b \]

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1. What is Division with Remainder?

Division with remainder (also called Euclidean division) is the process of dividing one integer (the dividend) by another (the divisor) to produce a quotient and a remainder. The remainder is always less than the divisor.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ \text{Quotient} = \left\lfloor\frac{a}{b}\right\rfloor \] \[ \text{Remainder} = a \bmod b \]

Where:

3. Applications of Division

Details: Division with remainder is fundamental in computer science (hashing, cryptography), number theory, and everyday arithmetic. It's the basis for modular arithmetic used in clock systems and cyclic patterns.

4. Using the Calculator

Tips: Enter two positive integers (dividend and divisor). The divisor must be greater than zero. The calculator will display both the integer quotient and the remainder.

5. Frequently Asked Questions (FAQ)

Q1: What happens if the divisor is zero?
A: Division by zero is undefined. The calculator requires the divisor to be at least 1.

Q2: How is this different from regular division?
A: Regular division can produce fractional results, while integer division gives whole number results with a remainder.

Q3: What's the relationship between quotient and remainder?
A: They satisfy: \( a = b \times \text{quotient} + \text{remainder} \) where \( 0 \leq \text{remainder} < b \).

Q4: Can I use negative numbers?
A: This calculator is designed for positive integers only, though the mathematical concept works for negatives.

Q5: What's the floor function?
A: It rounds down to the nearest integer (e.g., floor(7/3) = 2, floor(-1.5) = -2).

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