The given chemical formula is \(\mathrm{Fe}\left(\mathrm{ClO}_4\right)_4\).
Each \(\mathrm{ClO}_4\) (perchlorate) ion contains 1 chlorine atom.
Since there are 4 perchlorate ions in the formula unit, the total number of chlorine atoms is: \[ 4 \times 1 = 4 \]
\(\boxed{4}\)
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