Convert a base-10 number to octal. If the octal digits are divisible by 7, it's divisible by 7. IOW, 7 is octal's 9.
A number in base $n$ is just $a*n^2+b*n^1+c$.
Because $n mod n-1 = 1$, you can replace every $n$ with $1$.
So $a*n^2+b*n^1+c mod n-1$ becomes $a+b+c mod n-1$