Method of proof help

We have a regular   n-gone (polygon with N sides) whose tops are numbered 0,
1..., n-1, where top I follows the top i-1 in the anti-clockwise order. For
entire positive T < = N, an anti-clockwise rotation by an angle of 360t/n
degrees sends top 0 towards the top T.

Show that the smallest strictly positive number of anti-clockwise rotations
by 360t/n degrees which sends to the top 0 to itself is n/pgcd(t, n).

Deduct that N rotations anti-clockwise by 360t/n degrees are necessary to
send to the top 0 to itself if and only if PGCD(t, n)=1.