Frequently Asked Questions
What is a digital root?
The single digit you get by repeatedly summing the digits of a non-negative integer until only one remains.
Why does the mod 9 shortcut work?
Because 10 is congruent to 1 mod 9, every power of 10 is also congruent to 1 mod 9. So the sum of the digits of n is congruent to n mod 9, and after enough iterations you reach a single digit equal to n mod 9 (with 9 substituted when n mod 9 equals 0).
Is the digital root useful in real math?
Yes - it is a quick divisibility-by-9 check and a special case of digital invariants. It is also a classical pre-calculator way to spot arithmetic errors (casting out nines).
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