YouTube, the popular video hosting website logs all you activity. Which means YouTube has the list of videos that you have watched a couple of days ago. If you do not want your friends to find out what you watched some cute little girls or funny dogs on Youtube, you may want to make sure that the history is deleted by the time they use your computer and log out of public computers so that no one gets access to your data.
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There are actually two ways to find out about videos that a user has watched on YouTube.The browsing history of your web browser is the first location. You basically need to clear your browsing history and cache to make sure that no one can take a look at the data. You can do this either manually or by using utilities like CCleaner.

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To delete viewing history, log on to the Youtube website and go to this page. This page lists all the videos that you have watched on YouTube. You can remove individual videos from your history by selecting them and clicking the Remove button afterwards, or all videos with a click on “Clear all viewing history”.
If you have any doubts or suggestions, let me know via comments.