I can't open Excel,PP,word files in the sharepoint browser. I have installed only Sharepoint 2013 SP2 on premise and office 2016.
Can I open files without installing Office Web app?
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To be able to open documents in the browser you have to configure Office Web Apps.
An installation of Office 2016, will only enable you to open the specific file types locally on the machine you installed it on.
For further details on Office Web Apps with SP2013, please follow the guidelines given by Microsoft: https://technet.microsoft.com/en-us/library/ff431685.aspx