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Concentration of Risk and Segment Data - Segment Revenue and Income (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 28, 2019	Feb. 28, 2018	Feb. 28, 2019	Feb. 28, 2018
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Net revenue	$ 6,066,990	$ 5,301,101	$ 12,573,265	$ 10,886,633
Reconciling items:
Amortization of intangibles	(7,777)	(9,890)	(15,423)	(19,869)
Stock-based compensation expense and related charges	(15,697)	(15,039)	(32,946)	(67,784)
Restructuring and related charges	(817)	(5,427)	(6,842)	(16,815)
Other expense	(11,757)	(10,485)	(25,307)	(16,367)
Interest income	4,760	5,011	9,139	8,824
Interest expense	(46,160)	(37,796)	(88,812)	(74,042)
Income before income tax	100,826	86,262	265,713	193,701
Cayey, Puerto Rico
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Insurance recoveries		6,100	2,900	16,400
EMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Net revenue	3,804,727		7,307,830
Reconciling items:
Restructuring and related charges	(300)	(2,100)	(4,700)	(8,000)
DMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Net revenue	2,262,263		5,265,435
Reconciling items:
Restructuring and related charges	(500)	(3,300)	(2,100)	(7,900)
Operating Segments
Reconciling items:
Income before income tax	191,059	178,596	444,719	405,816
Operating Segments | EMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Net revenue	3,804,727	2,870,488	7,307,830	5,732,548
Reconciling items:
Income before income tax	88,654	95,283	172,749	180,993
Operating Segments | DMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Net revenue	2,262,263	2,430,613	5,265,435	5,154,085
Reconciling items:
Income before income tax	102,405	83,313	271,970	224,823
Segment Reconciling Items
Reconciling items:
Distressed Customer Charges	0	14,706	0	14,706
Stock-based compensation expense and related charges	(15,697)	(15,039)	(32,946)	(67,784)
Acquisition and integration charges	(12,785)	0	(21,675)	0
Business interruption and impairment charges, net(1)	$ 0	$ (4,002)	$ 2,860	$ (11,356)

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