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Concentration of Risk and Segment Data - Segment Revenue and Income (Details) - USD ($)
$ in Thousands
3 Months Ended
Nov. 30, 2018
Nov. 30, 2017
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Net revenue $ 6,506,275 $ 5,585,532
Reconciling items:    
Amortization of intangibles (7,646) (9,979)
Stock-based compensation expense and related charges (17,249) (52,745)
Restructuring and related charges (6,025) (11,388)
Other expense (13,550) (5,882)
Interest income 4,379 3,813
Interest expense (42,652) (36,246)
Income before income tax 164,887 107,439
Cayey, Puerto Rico    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Insurance recoveries 2,900 10,300
EMS    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Net revenue 3,503,103  
Reconciling items:    
Restructuring and related charges (4,400) (5,900)
DMS    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Net revenue 3,003,172  
Reconciling items:    
Restructuring and related charges (1,600) (4,600)
Operating Segments    
Reconciling items:    
Income before income tax 253,660 227,220
Operating Segments | EMS    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Net revenue 3,503,103 2,862,060
Reconciling items:    
Income before income tax 84,095 85,710
Operating Segments | DMS    
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]    
Net revenue 3,003,172 2,723,472
Reconciling items:    
Income before income tax 169,565 141,510
Segment Reconciling Items    
Reconciling items:    
Stock-based compensation expense and related charges (17,249) (52,745)
Acquisition and integration charges (8,890) 0
Business interruption and impairment charges, net(1) $ 2,860 $ (7,354)