Hey Antonio!
First of all, the correct spelling is "button."
"Button of the remote control" refers to a physical button that is part of the remote control itself.
"Button for the remote control" is not a common phrase. It might be used in a specific context, such as referring to a replacement button or a button that is used to operate the remote control indirectly (e.g., a voice command button).
However, in most cases, "button of the remote control" is the more natural and accurate phrase.
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