How to Calculate Modulo
What is Modulo?
Modulo (%) gives the remainder after division: a mod b = remainder of a ÷ b. It is fundamental to clock arithmetic, cryptography, hashing, cyclic patterns, and determining even/odd numbers. In programming, % is the modulo operator.
Step-by-Step Guide
- 117 mod 5 = 2 (because 17 = 3×5 + 2)
- 2Even numbers: n mod 2 = 0; Odd: n mod 2 = 1
- 3Clock arithmetic: (current hour + hours to add) mod 12
- 4Modular arithmetic: (a + b) mod n = ((a mod n) + (b mod n)) mod n
Worked Examples
Input
23 mod 7
Result
2
23 = 3×7 + 2
Input
100 mod 12 (clock)
Result
4
100 hours later = 4 AM
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