Divisible by 3 & 9: Why add the digits?

We've all seen the trick for figuring out whether a number is divisible by 3 or 9. But why does it work? Why can we just add up the digits?

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[xaxuser]

omg thank u i always wondered about that

[namelastname]

then why are any row, column or diagonal on the calculator always divisible by 3. Ie sum of digits are always divisible by 3?
for example 123, 147, 159.

[parthbhave]

Quite Intresting 😁 and love that dyed shirt given that I am a dyestuff technology student

[gamercrafts]

Thanks a lot ... Thats really helpful :)