Modulo Calculator
Calculate Remainder Operations
Calculate modulo (remainder) operations with detailed step-by-step explanations and visual breakdown.
Modulo Operation
Modulo Format:
a mod n
Also written as: a % n
What is Modulo?
The modulo operation finds the remainder after division of one number by another.
Formula:
a mod n = r
where r is the remainder
Example:
17 mod 5 = 2
Because 17 ÷ 5 = 3 remainder 2
Features
- Step-by-step solutions
- Detailed explanations
- Quotient and remainder
- Verification formula
- Quick examples
- Copy result
- Negative number support
- Decimal number support
Common Uses
Programming:
Check even/odd, array indexing
Cryptography:
Encryption algorithms
Time:
12-hour clock calculations
Mathematics:
Number theory, modular arithmetic
Properties
Range:
0 ≤ (a mod n) < n
Identity:
a mod 1 = 0
Self:
a mod a = 0
Distributive:
(a + b) mod n = ((a mod n) + (b mod n)) mod n
Use Cases
- Programming and algorithms
- Cryptography and security
- Hash functions
- Circular arrays and buffers
- Time and calendar calculations
- Check digit validation
- Random number generation
- Number theory problems
Examples
Real-World Examples:
Even/Odd:
n mod 2 = 0 (even) or 1 (odd)
12-Hour Clock:
15:00 mod 12 = 3:00 PM
Day of Week:
Day number mod 7 gives weekday
Array Wrap:
index mod length keeps in bounds
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