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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.

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1. 117 mod 5 = 2 (because 17 = 3×5 + 2)
2. 2Even numbers: n mod 2 = 0; Odd: n mod 2 = 1
3. 3Clock arithmetic: (current hour + hours to add) mod 12
4. 4Modular arithmetic: (a + b) mod n = ((a mod n) + (b mod n)) mod n

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