Given:
- Atomic number of Co = 27
- Oxidation state of Co in \([Co(NH_3)_6]^{3+}\) is \( +3 \)
- Each NH₃ ligand donates 2 electrons (but for EAN, we count only total ligand pairs = 6)
\[
\text{EAN} = 27 - 3 + 6 \times 2 = 24 + 12 = \boxed{36}
\]
Thus, cobalt achieves the effective atomic number of the nearest noble gas (Kr).