Consolidated Statements of Stockholders' Equity - USD ($) shares in Millions, $ in Millions	Total	Amount	Paid-in Capital	Retained Earnings	Accumulated Other Comprehensive Loss Items	Treasury Stock, at cost	ASC 606 adjustments	ASC 606 adjustments Retained Earnings
Beginning balance at Aug. 31, 2017	$ 1,665.6	$ 0.5	$ 881.0	$ 1,659.9	$ (99.7)	$ (776.1)
Beginning balance (in shares) at Aug. 31, 2017		41.8
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	349.6			349.6
Other comprehensive income (loss)	(4.0)				(4.0)
Reclassification of stranded tax effects of the Tax Cuts and Jobs Act				11.1	(11.1)
Share-based payment amortization, issuances, and cancellations (in shares)		0.2
Share-based payment amortization, issuances, and cancellations	23.7		23.6			0.1
Employee stock purchase plan issuances	0.6		0.6
Cash dividends paid on common stock	(21.4)			(21.4)
Stock options exercised	1.1
Repurchases of common stock (in shares)		(2.0)
Repurchases of common stock	(298.4)					(298.4)
Ending balance at Aug. 31, 2018	1,716.8	$ 0.5	906.3	1,999.2	(114.8)	(1,074.4)	$ (13.0)	$ (13.0)
Ending balance (in shares) at Aug. 31, 2018		40.0
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	330.4			330.4
Other comprehensive income (loss)	(36.6)				(36.6)
Share-based payment amortization, issuances, and cancellations (in shares)		0.2
Share-based payment amortization, issuances, and cancellations	23.1		23.1
Employee stock purchase plan issuances	0.6		0.6
Cash dividends paid on common stock	(20.8)			(20.8)
Repurchases of common stock (in shares)		(0.7)
Repurchases of common stock	(81.6)					(81.6)
Ending balance at Aug. 31, 2019	1,918.9	$ 0.5	930.0	2,295.8	(151.4)	(1,156.0)
Ending balance (in shares) at Aug. 31, 2019		39.5
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	248.3			248.3
Other comprehensive income (loss)	18.7				18.7
Share-based payment amortization, issuances, and cancellations (in shares)		0.1
Share-based payment amortization, issuances, and cancellations	32.7		32.7
Employee stock purchase plan issuances	0.8		0.8
Cash dividends paid on common stock	(20.8)			(20.8)
Stock options exercised	0.1		0.1
Repurchases of common stock (in shares)		(0.7)
Repurchases of common stock	(71.2)					(71.2)
Ending balance at Aug. 31, 2020	$ 2,127.5	$ 0.5	$ 963.6	$ 2,523.3	$ (132.7)	$ (1,227.2)
Ending balance (in shares) at Aug. 31, 2020		38.9