1. What is Modulus Operation?

The modulus operation finds the remainder after division of one number by another. In mathematics, the result is always non-negative and less than the divisor.

2. How Does Modulus Work?

The modulus operation is defined as:

Where:

• \( a \) — Dividend (the number being divided)
• \( b \) — Divisor (the number dividing by)
• \( \lfloor \rfloor \) — Floor function (rounds down to nearest integer)

Example: mod(17, 5) = 2 because 17 ÷ 5 = 3 with remainder 2

3. Applications of Modulus

Details: Modulus operations are widely used in:

• Computer programming (array indexing, hashing)
• Cryptography (RSA algorithm)
• Number theory (congruence relations)
• Time calculations (24-hour clock)
• Checking even/odd numbers

4. Using the Calculator

Tips: Enter any real numbers for dividend and divisor (divisor cannot be zero). The calculator will compute the remainder.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between modulus and remainder?
A: For positive numbers they're the same, but differ with negative numbers. Modulus is always non-negative.

Q2: Can the divisor be negative?
A: Yes, but the result will always be positive and less than the absolute value of the divisor.

Q3: What happens if divisor is zero?
A: Division by zero is undefined, so modulus by zero is also undefined.

Q4: How is modulus different from division?
A: Division gives the quotient, modulus gives the remainder.

Q5: Can modulus be used with floating-point numbers?
A: Yes, this calculator supports floating-point modulus operations.