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Goodwill and Other Intangible Assets (Changes in Goodwill Allocated to Segments) (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2021
Aug. 31, 2020
Goodwill [Roll Forward]    
Beginning balance $ 697 $ 622
Acquisitions and adjustments 17 62
Change in foreign currency exchange rates 1 13
Ending balance 715 697
EMS    
Goodwill [Roll Forward]    
Beginning balance 74 74
Acquisitions and adjustments 0 0
Change in foreign currency exchange rates 0 0
Ending balance 74 74
DMS    
Goodwill [Roll Forward]    
Beginning balance 623 548
Acquisitions and adjustments 17 62
Change in foreign currency exchange rates 1 13
Ending balance $ 641 $ 623