Reconciliation of Income Taxes at Federal Statutory Rate to Effective Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Federal statutory rate	21.00%	21.00%	21.00%
State income taxes, net of federal effect	0.70%	2.30%	(0.20%)
Net effects of foreign tax rate differential and credits	6.00%	1.30%	2.80%
Effective Income Tax Rate Reconciliation, FDII, Percent	(3.10%)	(4.50%)	(3.20%)
Effective Income Tax Rate Reconciliation, Compensation Adjustment	1.50%	6.60%	3.10%
Impairment and divestiture charges	0.00%	1.10%	1.60%
Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent	(0.80%)	2.10%	7.10%
Changes in liability for unrecognized tax benefits	(0.10%)	3.40%	(18.50%)
Effective Income Tax Rate Reconciliation, U.S. Legislative changes	0.00%	0.00%	(9.80%)
Net Benefit Taxable Liquidations of Subsidiaries Percent	0.10%	(11.40%)	0.00%
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent	1.70%	8.50%	1.20%
Effective Income Tax Rate Reconciliation, Change in Enacted Tax Rate, Percent	(2.00%)	(3.60%)	(3.40%)
Effective Income Tax Rate Reconciliation, Audits and Adjustments	(2.90%)	(6.70%)	8.00%
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Research and Development, Percent	(0.70%)	(2.50%)	(1.80%)
Other items	0.70%	0.70%	0.70%
Effective income tax rate	22.10%	18.30%	8.60%
Impairment and divestiture (benefit) charges	$ (6,155)	$ 2,413	$ 6,198
Net Benefit, Taxable Liquidations of Foreign Subsidiaries		(2,700)
Effective Income Tax Rate Reconciliation, Withholding Tax, Foreign, Amount	1,600	200	1,100
Non-Cash Impairment charges - foreign earnings		1,100	1,500
Effective Income Tax Rate Reconciliation audits and adjustments, amount	$ 2,000	$ 1,600	$ 3,500