Modulo Calculator
Calculate modulo (remainder) and quotient. Understand mathematical mod operation vs JavaScript remainder. Free online modulo calculator.
Common Examples
| Expression | Result | Explanation |
|---|---|---|
| 17 mod 5 | 2 | 17 = 3×5 + 2 |
| 10 mod 3 | 1 | 10 = 3×3 + 1 |
| 100 mod 7 | 2 | 100 = 14×7 + 2 |
| -7 mod 3 | 2 | -7 = -3×3 + 2 |
| 15 mod 15 | 0 | Perfectly divisible |
Common Use Cases
Check if even/odd: n mod 2 = 0 → even, n mod 2 = 1 → odd
Clock arithmetic: (hour + n) mod 12 for 12-hour clock
Circular arrays: index mod length wraps around
Divisibility: a mod b = 0 means b divides a evenly
Digit extraction: n mod 10 gives last digit
Modulo Properties
Identity: a mod 1 = 0
Self: a mod a = 0
Smaller: a mod b = a (if |a| < |b|)
Additive: (a + b) mod n = ((a mod n) + (b mod n)) mod n
Multiplicative: (a × b) mod n = ((a mod n) × (b mod n)) mod n
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