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
Because nine is one less than ten, and we work in a base ten system.
132,189 means:
> One hundred and thirty-two thousand, one hundred and eighty-nine
Or in terms of symbols:
> 1 * 10^5 + 3 * 10^4 + 2 * 10^3 + 1 * 10^2 + 8 * 10^1 + 9 * 10^0
So let’s look at our most general number:
> a + b * 10 + c * 100 + d * 1000 + e * 10,000 + …
The sum of the digits of this number will be:
> a + b + c + d + e + …
So if we take that away from the number itself we will get:
> b * 9 + c * 99 + d * 999 + e * 9999 + …. = 9(b + 11c + 111d + 1111e + …)
Meaning the difference between any number and the sum of its digits will always be a multiple of nine!
Now if we have a number that is n modulo 9, and we take away a multiple of 9 from that number, our new number will still be n modulo 9 (that’s kind of what modulo 9 means).
So if our original number is n modulo 9, then the sum of its digits will also be n modulo 9 (as that is a multiple of 9 less than our starting number), as will the sum of the digits of the sum of the digits, and so on.
Now if we have a number that is n modulo 9, and we take away a multiple of 9 from that number, our new number will still be n modulo 9 (that’s kind of what modulo 9 means).
So if our original number is n modulo 9, then the sum of its digits will also be n modulo 9 (as that is a multiple of 9 less than our starting number), as will the sum of the digits of the sum of the digits, and so on.
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