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I have read that branches need to be named in alphabetical order, but I do not really understand this, or do you start with the branch closest to the edge of the hydrocarbon?

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Branches must be numbered in alphabetical order, along with their positions. Suppose you have a chloro group on the first carbon, a bromo group on the second carbon and an amino group on the fourth carbon of your carbon chain (butane). One must therefore go in alphabetical order which is amino, then bromo and then chloro. Therefore you naming will be something like this:-

$$\ce{3-Bromo-4-chloro-butanamine}$$

The naming is in alphabetical order but the numbering starts according to the following rule:

$$\ce{RCOOH>RCOOR>RCOCOOR>RCOCl>RCONH2>RCHO>CO>OH>NH2>double bond>triple bond>halogen>NO2>ROR>alkyl}$$

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