Q: Apply the first isomorphism theorem to φ: ℤ → ℤ₆, φ(k) = k mod 6. φ(a+b) = (a+b) mod 6 ✓: homomorphism! Kernel: multiples of 6: 6ℤ! Image: all of ℤ₆ (surjective!). ℤ/6ℤ ≅ ℤ₆! (Collapsing kernel gives the image!)