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
It’s because our numbers are in base 10, and we only have 9 digits.
When we have 9 of something and add one, we represent that as 1 ‘ten’ and zero ones. So the sum of the digits between 9 and 10 goes from 9 back to 1. This is the core of modulo 9.
The pattern continues for all numbers – the sums will climb and then drop every time you cross a threshold from a number ending in a 9 to one ending in a zero.
The pattern even works when you cross multiple thresholds at once, as you’re just doing this drop from a nine to a one multiple times.
For example, when you go from 99 to 100, the 9 in the ones place turns into a one in the tens place. That in turn makes that nine into a one in the hundreds place. Once more, you’ve lost two sets of nine and gone back to one – in terms of digit sums, you’re going from 99; 9+9 = 18; 1+8 = 9, back to 100; 1+0+0 = 1 again.
So modulo 9 is baked into our number system because there is no single digit that is bigger than 9 – we just shift positions over and start back at 1.
Any given number is made up of some amount of 9s and then some extra ones. Doing successive digit addition or modulo 9 are equivalent ways of getting rid of sets of nine until you see what’s left.
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