Modulo gives the remainder after division: 17 mod 5 = 2 (because 17 = 5×3 + 2). It's fundamental in programming (array indexing, hash tables), cryptography (RSA), and everyday life (clock arithmetic: 15:00 mod 12 = 3 PM).
How to Use
Enter dividend and divisor:
- a mod b: Remainder of a ÷ b
- Quotient: Floor division result
- Verification: a = b × quotient + remainder
Negative Numbers
Languages differ: -7 mod 3 = -1 (C/Java/JS) or 2 (Python). Math convention: result has same sign as divisor. We show both interpretations.
Applications
- Clock math: hour mod 12
- Even/odd: n mod 2
- Cycling: index mod arrayLength
- Check digits: ISBN mod 11
- Cryptography: RSA uses modular exponentiation
Step-by-Step Instructions
- 1Enter the dividend (a).
- 2Enter the divisor (b).
- 3View the remainder (a mod b).
- 4Check the step-by-step division.
- 5Try negative number behavior.