Modulo Calculator
Calculate the modulo (remainder) of division operations with detailed explanations.
Modulo Operation
What is Modulo?
The modulo operation finds the remainder after division of one number by another.
a mod n = r
where r is the remainder
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
Check even/odd, array indexing
Encryption algorithms
12-hour clock calculations
Number theory, modular arithmetic
Properties
0 ≤ (a mod n) < n
a mod 1 = 0
a mod a = 0
(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:
n mod 2 = 0 (even) or 1 (odd)
15:00 mod 12 = 3:00 PM
Day number mod 7 gives weekday
index mod length keeps in bounds
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