Digital Roots

What is a Digital Root?

The Digital Root of a number is the single digit obtained by repeatedly adding the digits of the number until a single digit remains.

Example: Find the digital root of $489710$.

1. Sum 1: $4 + 8 + 9 + 7 + 1 + 0 = 29$
2. Sum 2: $2 + 9 = 11$
3. Sum 3: $1 + 1 = 2$ Digital Root = 2

Properties

1. Divisibility by 9: If the Digital Root is 9, the number is divisible by 9.
2. Remainders: The Digital Root is equivalent to the remainder when the number is divided by 9.
   • Exception: If the remainder is 0, the Digital Root is 9.

Pattern in Consecutive Numbers

Digital roots follow a repeating cycle: $1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, \dots$