1. What is Quotient and Remainder?

The quotient and remainder are the two main results of integer division. The quotient represents how many times the divisor fits completely into the dividend, while the remainder is what's left over.

2. How Does the Calculator Work?

The calculator uses the division algorithm:

Where:

• \( a \) — Dividend (the number being divided)
• \( b \) — Divisor (the number dividing by)
• \( q \) — Quotient (integer result of division)
• \( r \) — Remainder (amount left over)

Explanation: The algorithm guarantees that the remainder is always less than the divisor and non-negative.

3. Importance of Division Algorithm

Details: The division algorithm is fundamental in number theory and computer science, used in modular arithmetic, cryptography, and hash functions.

4. Using the Calculator

Tips: Enter positive integers for both dividend and divisor. The divisor must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What happens with negative numbers?
A: This calculator uses floor division, which always rounds down. For negative numbers, the remainder will still be non-negative.

Q2: How is this different from regular division?
A: Integer division gives whole number results, while regular division can produce fractions/decimals.

Q3: What's the relationship between modulo and remainder?
A: The modulo operation directly gives the remainder of division. In most programming languages, % is the modulo operator.

Q4: Can the remainder be zero?
A: Yes, when the dividend is exactly divisible by the divisor (e.g., 10 ÷ 2 = 5 with remainder 0).

Q5: What's the maximum possible remainder?
A: The remainder is always less than the divisor, so the maximum possible remainder is (divisor - 1).