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Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 30, 2021
Nov. 30, 2020
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Income $ 317 $ 285
Reconciling items:    
Amortization of Intangible Assets (8) (11)
Stock-based compensation expense and related charges (35) (34)
Restructuring, severance and related charges 0 1
Interest income 1 2
Interest Expense (33) (32)
Operating Segments    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Income 400 365
Operating Segments | EMS    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Income 147 122
Operating Segments | DMS    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Income 253 243
Segment Reconciling Items    
Reconciling items:    
Amortization of Intangible Assets (8) (11)
Stock-based compensation expense and related charges (35) (34)
Restructuring, severance and related charges 0 1
Acquisition and integration charges 0 (2)
Other expense (net of periodic benefit cost) (8) (4)
Interest income 1 2
Interest Expense $ (33) $ (32)