Reconciliation of Income Taxes at Federal Statutory Rate to Effective Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Federal statutory rate	21.00%	21.00%	21.00%
State income taxes, net of federal effect	1.30%	0.70%	2.30%
Net effects of foreign tax rate differential and credits	4.20%	6.00%	1.30%
Effective Income Tax Rate Reconciliation, FDII, Percent	(2.30%)	(3.10%)	(4.50%)
Effective Income Tax Rate Reconciliation, Compensation Adjustment	2.00%	1.50%	6.60%
Impairment and divestiture charges	0.00%	0.00%	1.10%
Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent	(4.10%)	(0.80%)	2.10%
Changes in liability for unrecognized tax benefits	(1.30%)	(0.10%)	3.40%
Effective Income Tax Rate Reconciliation, U.S. Legislative changes	1.60%	0.00%	0.00%
Net Benefit Taxable Liquidations of Subsidiaries Percent	0.00%	0.10%	(11.40%)
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent	0.30%	1.70%	8.50%
Effective Income Tax Rate Reconciliation, Change in Enacted Tax Rate, Percent	0.00%	(2.00%)	(3.60%)
Effective Income Tax Rate Reconciliation, Audits and Adjustments	0.40%	(2.90%)	(6.70%)
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Research and Development, Percent	(0.60%)	(0.70%)	(2.50%)
Other items	(0.40%)	0.70%	0.70%
Effective income tax rate	22.10%	22.10%	18.30%
Impairment and divestiture (benefit) charges	$ 147	$ (6,155)	$ 2,413
Net Benefit, Taxable Liquidations of Foreign Subsidiaries			2,700
Effective Income Tax Rate Reconciliation, Withholding Tax, Foreign, Amount	3,400	2,600	1,500
Non-Cash Impairment charges - foreign earnings			1,100
Effective Income Tax Rate Reconciliation audits and adjustments, amount	$ 400	$ 2,000	$ 1,600