it increase earnings per share (because fewer shares), which can in turn can increase stock price.
it reduces the number of shareholders or their power, meaning that the board has fewer people telling it what to do. Buying out all/most of the stock means making company private, partial buyback is a step towards that.
there are a few other reasons:
https://www.investopedia.com/ask/answers/042015/why-would-company-buyback-its-own-shares.asp
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