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Income Taxes (Details) - USD ($)	12 Months Ended			24 Months Ended
	Aug. 31, 2020	Aug. 31, 2019	Aug. 31, 2018	Aug. 31, 2019
Effective Income Tax Rate Reconciliation, Amount [Abstract]
Federal income tax computed at statutory rate	$ 68,200,000	$ 89,200,000	$ 109,400,000
State income tax, net of federal income tax benefit	9,700,000	12,200,000	11,500,000
Foreign permanent differences and rate differential	2,400,000	2,100,000	(2,000,000.0)
Research and development tax credits	(7,100,000)	(18,100,000)	(3,300,000)
Unrecognized tax benefits	1,800,000	12,200,000	400,000
Other, net	1,400,000	(900,000)	(5,100,000)
Total provision for income taxes	76,400,000	94,500,000	76,300,000
Effective Income Tax Rate Reconciliation, Tax Cuts and Jobs Act, Amount	0	(2,200,000)	(34,600,000)
Deferred income tax liabilities:
Depreciation	(23,300,000)	(22,000,000.0)		$ (22,000,000.0)
Goodwill and intangibles	(153,100,000)	(149,600,000)		(149,600,000)
Operating lease right of use asset	(15,600,000)
Other liabilities	(5,300,000)	(2,800,000)		(2,800,000)
Total deferred income tax liabilities	(197,300,000)	(174,400,000)		(174,400,000)
Deferred income tax assets:
Self-insurance	2,100,000	2,600,000		2,600,000
Pension	22,200,000	22,700,000		22,700,000
Deferred compensation	22,200,000	20,500,000		20,500,000
Net operating losses	5,600,000	6,200,000		6,200,000
Other accruals not yet deductible	32,000,000.0	26,900,000		26,900,000
Operating lease liabilities	18,200,000
Other assets	9,300,000	9,700,000		9,700,000
Total deferred income tax assets	111,600,000	88,600,000		88,600,000
Valuation allowance	(6,500,000)	(4,600,000)		(4,600,000)
Net deferred income tax liabilities	(92,200,000)	(90,400,000)		(90,400,000)
Undistributed earnings and original investments in foreign subsidiaries	144,900,000	144,900,000		144,900,000
Deferred income tax liability for certain foreign withholding taxes and U.S. state taxes	2,900,000
Tax benefit related to the enactment of the TCJA				36,800,000
Tax benefit to decrease deferred income taxes to the revised statutory rate				32,500,000
Current estimated benefit for transition tax				4,300,000
State tax credit carryforwards	1,600,000
Unrecognized tax benefits	17,200,000	16,600,000	$ 4,400,000	16,600,000
Unrecognized tax benefits that if recognized would affect annual effective tax rate	16,700,000	15,900,000		15,900,000
Total accrued interest	1,700,000	$ 1,000,000.0		$ 1,000,000.0
Accruals related to income tax penalties	0
Internal Revenue Service (IRS)
Deferred income tax assets:
Operating loss carryforwards	32,000,000.0
State and Local Jurisdiction
Deferred income tax assets:
Operating loss carryforwards	21,200,000
Foreign Tax Authority
Deferred income tax assets:
Operating loss carryforwards	$ 2,900,000

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