Digit sum: sum of all digits (e.g., 493 → 4+9+3 = 16). Digital root: repeat until single digit (493 → 16 → 7). Formula: dr(n) = 1 + (n−1) mod 9. Additive persistence: how many iterations to reach digital root. Multiplicative persistence: multiply digits instead.
How to Use
Enter any number:
- Input: Positive integer
- Output: Digit sum, root, persistence
- Extra: Digit frequency and product
Divisibility Tests
- Divisible by 3 ↔ digit sum divisible by 3
- Divisible by 9 ↔ digit sum divisible by 9
- Digital root = remainder mod 9 (except 0→9)
Persistence
Additive persistence of 199: 1+9+9=19, 1+9=10, 1+0=1 → persistence = 3. Multiplicative: 39 → 27 → 14 → 4 → persistence = 3.
Step-by-Step Instructions
- 1Enter a number.
- 2View digit sum.
- 3Check digital root.
- 4See persistence count.
- 5Explore digit frequency.