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Explanation:
There are two carbons, so the root of the name will be '-ethane'
We need to number the carbon atoms
1
or
2
, so I'll choose the carbon bonded to Br, Cl and F to be the first carbon, since it has the most non-hydrogen substituents on it.
Therefore, there is one chlorine on the 1-carbon, one bromine on the 1-carbon, and one fluorine on the 1-carbon. There are also two fluorines on the 2-carbon, so we have:
1-chloro
1-bromo
1,2,2-trifluoro
and,
ethane
We list the prefixes in the IUPAC name in alphabetical order, so in full it is
1-bromo-1-chloro-1,2,2-trifluoroethane.