See also this thread, which is very relevant as it is all about exactly this type of calculation:

Analyzing Rüdiger Gamms performance (division by 109)
Mental Calculation, Mathematics, and Puzzles
While watching YouTube videos’of Rüdiger Gamms performance in order to find out how he does the higher powers I realized something. In at least three video’s I saw him do a division by 109. There is a reason for this. One example is this video: ...
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