Modulo

Modulo, denoted by the symbol "%", is a mathematical operation that finds the remainder when one number is divided by another. It is commonly used in computer programming and mathematical calculations.

Modulo Operation

The modulo operation is performed using the following formula:

a % b = r

Where:

• a is the dividend (the number being divided)
• b is the divisor (the number by which a is being divided)
• r is the remainder

Examples

For example, if we have the operation 11 % 3, the result would be 2 because 11 divided by 3 equals 3 with a remainder of 2.

Another example would be 15 % 4, which equals 3 because 15 divided by 4 equals 3 with a remainder of 3.

Properties of Modulo

Some important properties of the modulo operation include:

• Commutative property: a % b = b % a
• Associative property: (a % b) % c = a % (b % c)
• Distributive property: a % (b + c) = (a % b + a % c) % a

Applications

Modulo operation has various applications, including:

• Checking divisibility
• Generating random numbers
• Calculating recurring patterns and cycles
• Encrypting and decrypting data

Study Guide

Here are some key points to remember when studying modulo:

1. Understand the concept of remainder in division.
2. Practice solving modulo operations using different numbers.
3. Learn the properties of modulo and how they can be applied in calculations.
4. Explore real-world applications of modulo in computer science and mathematics.

By understanding the modulo operation and its applications, you can improve your problem-solving skills and computational abilities.