Q: Find all generators of ℤ₆. Find all subgroups of ℤ₆. Generators: a with gcd(a,6) = 1: {1,5} (φ(6) = 2!). Subgroups: ⟨d⟩ for d|6: ⟨0⟩={0}, ⟨3⟩={0,3}, ⟨2⟩={0,2,4}, ⟨1⟩=ℤ₆. Orders: 1, 2, 3, 6 (all divide 6!). (Cyclic: subgroups correspond to divisors!)