2016 Digital Root

Number Theory Level 1

For each number \(n\), we define the Digital Root of \(n\) in the following manner: Take the sum of the digits to obtain a new number. Repeat this process until the result is a single digit.

Find the digital root of \(\underset { 2016\text{ times} }{ \underbrace { 2016\ldots2016 } } \).

As an explicit example, for \(n=3487\), \[3487\quad \rightarrow \quad 3+4+8+7=22\quad \rightarrow \quad 2+2=4 \; . \] Therefore, the digital root of 3487 is 4.

Clarification: In the number above, 2016 appears 2016 times in its decimal representation.


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