Modulo Calculator – Calculate and Find Remainders

What Is a Modulo Operation?

The modulo operation, often written as X mod Y, returns the remainder when one number is divided by another. It is a foundational concept in number theory and has practical applications in fields such as cryptography, computer science, finance, and scheduling. It's a quick way to solve problems like:

• What’s the remainder when 23 is divided by 5?
• What is 100 mod 7?

In math, this operation is called "modulus" or simply "mod" The result tells you what is left after division.

How to Use the Modulo Calculator

1. Enter the dividend (number to divide).
2. Enter the divisor.
3. Click "Calculate" to see the remainder and breakdown.

Real-Life Uses of Modulo

• Programming logic (e.g. even/odd checks)
• Time conversions (e.g. 130 minutes is 2 hours and 10 minutes)
• Math homework and number theory
• Scheduling and repeating intervals

Formula:

The modulo formula is: a mod b = r

Where:

• a = dividend
• b = divisor
• r = remainder

So, if a = 12 and b = 5, then 12 mod 5 = 2.

Mathematical Properties

• If X is divisible by Y, then X mod Y = 0.
• Modulo is non-negative when both X and Y are positive.
• (a + b) mod n = ((a mod n) + (b mod n)) mod n (Modular addition)
• (a × b) mod n = ((a mod n) × (b mod n)) mod n (Modular multiplication)