heres what i mean:
132189 –> 1 + 3 + 2 + 1 + 8 + 9 = 24 –> 2 + 4 = 6
132189 % 9 = 6
https://en.wikipedia.org/wiki/Digital_root
In: 7
First, don be confused by the name, “digital root” is only distantly related to concepts like root of square numbers or the concept of digital in computers.
It just means taking the digit sum over and over again until you have just a single digit left.
Due to the way decimal works, you can tell if a number is divisible by 9 or 3, by looking at its digit sum.
Every time you add 9 to a number ending on 0. you increase its digit sum by 9
Every time you add 9 to a number ending on a last digit larger than 0 you subtract one from the last digit and add one to the 2nd last one. If that 2nd last digit is already 9 it becomes zero and the next one gets one added. And so on.
In any case adding 9 either keeps the digit sum the same or adds or subtracts multiples of 9.
So taking the digit sum of a number that is divisible by 9 without rest results in a smaller number also divisible by 9 without rest.
Any rest from 1 to 8 you add to a number divisible by 9 will be preserved in either the modulo or the digital root method.
This is useful to tell if a large number is divisible by 9 (or 3 if the digital root is 3 or 6 or 0/9).
This is just an aspect of our decimal system. In hex you can take the digit sum of a number to figure out if it is divisible by 15 or (5 or 3). In octal it would be 7.
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