Digital Root (Mod 9)
A number's remainder mod 9 is the same as its digit sum's remainder.
4573 mod 9 = 1
Every power of ten leaves remainder 1 against 9, so each digit counts itself.
Add the digits: 19. Still two digits, so fold again: 1 + 9 = 10, then 1.
That last single digit is the remainder: 4573 leaves 1 when divided by 9.
Your turn
Three to try in your head — tap what you get.
9064 mod 3
8426 mod 3
5550 mod 9
All 36 shortcuts: the Magic Tricks library.