1. What is the Modulus Operation?

The modulus operation finds the remainder after division of one number by another. In programming and mathematics, it's often represented by the '%' symbol or 'mod' keyword.

2. How Does the Calculator Work?

The calculator uses the modulus formula:

Where:

• \( a \) — Dividend (the number being divided)
• \( b \) — Divisor (the number dividing by)
• The result is always between 0 and \( b \)

Example: 7 mod 3 = 1 because 7 divided by 3 equals 2 with a remainder of 1.

3. Importance of Modulus Calculation

Details: The modulus operation is fundamental in computer science for tasks like determining even/odd numbers, circular arrays, hashing algorithms, and cryptography.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between modulo and remainder?
A: For positive numbers they're identical. For negative numbers, modulo always returns a positive result between 0 and the divisor.

Q2: Can the divisor be zero?
A: No, division by zero is undefined in mathematics. The calculator will show an error if you attempt this.

Q3: How is modulus used in programming?
A: Common uses include checking for even numbers (n % 2 == 0), array indexing, and generating random numbers within a range.

Q4: What about negative numbers?
A: The calculator handles negative numbers correctly according to mathematical modulo operation rules.

Q5: Is there a difference between '%' and 'mod'?
A: In most programming languages, '%' is the modulus operator, while 'mod' is often used in mathematical notation.