1. **Problem Statement:** Find the digital root of a number by repeatedly summing its digits until a single digit (1 to 9) remains. 2. **Definition:** The digital root of a number is the single digit obtained by iteratively summing the digits of the number. 3. **Example Calculations:** - For 71: $7 + 1 = 8$, so the digital root is $8$. - For 231: $2 + 3 + 1 = 6$, so the digital root is $6$. - For 85: $8 + 5 = 13$, then $1 + 3 = 4$, so the digital root is $4$. - For 7562: $7 + 5 + 6 + 2 = 20$, then $2 + 0 = 2$, so the digital root is $2$. 4. **General Formula:** The digital root of a positive integer $n$ can be found using the formula: $$\text{digital root}(n) = 1 + ((n - 1) \bmod 9)$$ This formula works because the digital root is congruent to $n$ modulo 9, except that the digital root of multiples of 9 is 9, not 0. 5. **Explanation:** - Sum the digits of the number. - If the result is a single digit, that is the digital root. - If not, repeat the summing process until a single digit is obtained. 6. **Summary:** The digital root is a way to reduce any number to a single digit by summing its digits repeatedly. **Final answer:** The digital root of a number $n$ is given by $$1 + ((n - 1) \bmod 9)$$ or by iterative summation of digits until one digit remains.