1. What is Modulo Operation?

The modulo operation finds the remainder after division of one number by another. Given two numbers, a (the dividend) and b (the divisor), a modulo b is the remainder of the Euclidean division of a by b.

2. How Does the Calculator Work?

The calculator uses the modulo operation:

Where:

• \( a \) — The dividend
• \( b \) — The divisor (must be non-zero)
• \( mod \) — The remainder after division

Explanation: The operation returns the remainder of dividing a by b. For example, 7 mod 3 = 1 because 7 divided by 3 equals 2 with a remainder of 1.

3. Importance of Modulo Calculation

Details: Modulo operations are fundamental in computer science, cryptography, and number theory. They're used for hashing, generating random numbers, circular arrays, and determining if numbers are even or odd.

4. Using the Calculator

Tips: Enter any number for a (dividend) and a non-zero number for b (divisor). The calculator will compute the remainder of a divided by b.

5. Frequently Asked Questions (FAQ)

Q1: What happens if b is zero?
A: Division by zero is undefined, so the calculator requires b to be non-zero.

Q2: How does modulo work with negative numbers?
A: The result takes the sign of the dividend (a). For example, -7 mod 3 = -1, while 7 mod -3 = 1.

Q3: What's the difference between modulo and remainder?
A: For positive numbers they're the same, but they differ in handling of negative numbers in some programming languages.

Q4: What are common uses of modulo?
A: Checking even/odd numbers, wrapping values within a range, cryptography algorithms, and hash table implementations.

Q5: How is modulo implemented in programming languages?
A: Most languages use % operator (e.g., a % b), but behavior with negatives varies between languages.