Long Division Calculator
÷
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.
💡
Tip: In Python, -7 % 3 = 2 (not -1). Python always returns a non-negative result for positive modulus. In C/Java, -7 % 3 = -1. This difference causes bugs — always test with negative numbers.
- 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
23 mod 7=223 = 3×7 + 2
100 mod 12 (clock)=4100 hours later = 4 AM
| Application | Formula | Example |
|---|---|---|
| Even/odd check | n mod 2 | 17 mod 2 = 1 (odd) |
| Clock hours | (h + n) mod 12 | (10 + 5) mod 12 = 3 |
| Day of week | (day + n) mod 7 | Mon + 10 days = Thu |
| Array wraparound | index mod length | 7 mod 5 = 2 |
| Checksums | sum mod n | Credit card validation |
| Cryptography | a^e mod n | RSA encryption |
⭐
Fun Fact
The ISBN-13 barcode uses modulo 10 for its check digit: multiply alternate digits by 1 and 3, sum them, and the check digit makes the total divisible by 10. This detects single-digit errors with 100% accuracy.
References
🔒
୧୦୦% ମାଗଣା
ପଞ୍ଜୀକରଣ ଆବଶ୍ୟକ ନାହିଁ
✓
ସଠିକ
ଯାଞ୍ଚ ହୋଇଥିବା ସୂତ୍ର
⚡
ତତ୍କ୍ଷଣ
ତତ୍କ୍ଷଣ ଫଳ
📱
ମୋବାଇଲ୍ ଅନୁକୂଳ
ସମସ୍ତ ଡିଭାଇସ୍