Step 1: Recall electronic configuration of Mn.
Manganese (\(Z=25\)) has the electronic configuration:
\[
[Ar] \, 3d^5 \, 4s^2
\]
Step 2: Possible oxidation states.
Manganese exhibits a wide range of oxidation states from +2 to +7, due to variable involvement of 3d and 4s electrons.
Step 3: Most common oxidation states.
- \(+2\): This state arises from loss of 4s electrons. Example: MnCl$_2$. This is very common and stable.
- \(+4\): This state arises from loss of 4s and two 3d electrons. Example: MnO$_2$. This is also very common in nature.
Other states (+5, +6, +7) exist but are less stable and less frequently encountered in common compounds. The highest oxidation state +7 is found in KMnO$_4$, but it is not as commonly occurring as +2 and +4.
Step 4: Final Answer.
Hence, the most common oxidation states of manganese are +2 and +4.
\[
\boxed{+2, +4}
\]
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