Step 1: Meaning of equilibrium constant.
If \(K\) is very large (\(K \gg 1\)), equilibrium lies far to the right, meaning products dominate.
If \(K \ll 1\), reactants dominate.
Step 2: Compare values.
\[
10^2 = 100,\quad 10,\quad 10^{-2}=0.01,\quad 1
\]
Largest value is \(100\).
Step 3: Conclusion.
So reaction goes farthest to completion when \(K = 10^2\).
Final Answer:
\[
\boxed{K = 10^2}
\]