Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 28, 2022	Feb. 28, 2021	Feb. 28, 2022	Feb. 28, 2021
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	$ 284	$ 209	$ 601	$ 494
Reconciling items:
Amortization of intangibles	(8)	(12)	(16)	(23)
Stock-based compensation expense and related charges	(16)	(23)	(51)	(57)
Restructuring, severance and related charges	0	(6)	0	(5)
Interest income	0	2	1	4
Interest expense	(33)	(31)	(66)	(63)
Operating Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	344	285	744	650
Operating Segments | EMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	152	98	299	220
Operating Segments | DMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Income	192	187	445	430
Segment Reconciling Items
Reconciling items:
Amortization of intangibles	(8)	(12)	(16)	(23)
Stock-based compensation expense and related charges	(16)	(23)	(51)	(57)
Restructuring, severance and related charges	0	(6)	0	(5)
Business interruption and impairment charges, net	0	1	0	1
Acquisition and integration charges	0	(2)	0	(4)
Other expense (net of periodic benefit cost)	(3)	(5)	(11)	(9)
Interest income	0	2	1	4
Interest expense	$ (33)	$ (31)	$ (66)	$ (63)