Reconciliation of Income Taxes at Federal Statutory Rate to Effective Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020	Aug. 31, 2019
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Federal statutory rate	21.00%	21.00%	21.00%
State income taxes, net of federal effect	2.30%	(0.20%)	(0.60%)
Net effects of foreign tax rate differential and credits	1.30%	2.80%	38.70%
Effective Income Tax Rate Reconciliation, Foreign derived intangible income deduction, Percent	(4.50%)	(3.20%)	0.00%
Effective Income Tax Rate Reconciliation, Compensation Adjustment	6.60%	3.10%	6.60%
Impairment and divestiture charges	1.10%	1.60%	3.30%
Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent	2.10%	7.10%	(8.10%)
Changes in liability for unrecognized tax benefits	3.40%	(18.50%)	(5.30%)
Effective Income Tax Rate Reconciliation, U.S. Legislative changes	0.00%	(9.80%)	(32.50%)
Net Benefit Taxable Liquidations of Subsidiaries Percent	(11.40%)	0.00%	52.60%
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent	8.50%	1.20%	7.40%
Effective Income Tax Rate Reconciliation, Change in Enacted Tax Rate, Percent	(3.60%)	(3.40%)	(9.00%)
Effective Income Tax Rate Reconciliation, Audits and Adjustments	(6.70%)	8.00%	(27.40%)
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Research and Development, Percent	(2.50%)	(1.80%)	(11.50%)
Other items	0.70%	0.70%	(6.00%)
Effective income tax rate	18.30%	8.60%	29.20%
Effective Income Tax Rate Reconciliation, Tax Credit, Foreign, Amount	$ 2,300	$ 4,600	$ 4,000
Impairment and divestiture (benefit) charges	2,413	6,198	(3,159)	$ (3,200)
Impairment, Non-Deductible for Income Tax Purposes	1,300	3,500	300
SEC Schedule, 12-09, Valuation Allowances and Reserves, Additions, Charge to Cost and Expense	900	4,900	9,400
SEC Schedule, 12-09, Valuation Allowances and Reserves, Deduction	5,500	9,100	12,300
Net Benefit, Taxable Liquidations of Foreign Subsidiaries	(2,700)		4,100
Effective Income Tax Rate Reconciliation, Withholding Tax, Foreign, Amount	1,300	1,700	5,400
Non-Cash Impairment charges - foreign earnings	1,100	1,500	(600)
Effective Income Tax Rate Reconciliation audits and adjustments, amount	$ 1,600	$ 3,500	$ 2,200