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), resulting in a quotient and a remainder that is less than the divisor in absolute value.

2. How Does the Calculator Work?

The calculator uses integer division and modulo operation:

Where:

• \( a \) — Dividend (integer)
• \( b \) — Divisor (non-zero integer)
• \( q \) — Quotient (integer)
• \( r \) — Remainder (0 ≤ r < |b|)

Explanation: The division satisfies \( a = b \times q + r \) where \( 0 \leq r < |b| \).

3. Importance of Remainder Calculation

Details: Remainder calculations are fundamental in number theory, computer science (for hashing and modular arithmetic), and many algorithms. They're used in cryptography, calendar calculations, and cyclic operations.

4. Using the Calculator

Tips: Enter two integers (dividend and divisor). The divisor cannot be zero. The calculator will return both the integer quotient and remainder.

5. Frequently Asked Questions (FAQ)

Q1: What happens if the divisor is zero?
A: Division by zero is undefined. The calculator will not return a result if zero is entered as the divisor.

Q2: How is remainder different from decimal division?
A: Remainder gives the whole number left over after division, while decimal division continues into fractional parts.

Q3: What's the difference between modulo and remainder?
A: For positive numbers they're the same. For negative numbers, modulo always returns a non-negative result.

Q4: Where is this used in programming?
A: Commonly used for determining even/odd (n % 2), circular array indexing, hash functions, and many algorithms.

Q5: Can this work with negative numbers?
A: Yes, the calculator handles negative dividends and divisors correctly according to mathematical definitions.