Reconciliation of Income Taxes at Federal Statutory Rate to Effective Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Federal statutory rate	21.00%	21.00%	21.00%
State income taxes, net of federal effect	0.20%	1.30%	0.70%
Net effects of foreign tax rate differential and credits	3.30%	4.20%	6.00%
Effective Income Tax Rate Reconciliation, FDII, Percent	(1.90%)	(2.30%)	(3.10%)
Effective Income Tax Rate Reconciliation, Compensation Adjustment	0.70%	2.00%	1.50%
Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent	0.00%	(4.10%)	(0.80%)
Changes in liability for unrecognized tax benefits	0.20%	(1.30%)	(0.10%)
Effective Income Tax Rate Reconciliation, U.S. Legislative changes	(0.70%)	1.60%	0.00%
Net Benefit Taxable Liquidations of Subsidiaries Percent	0.00%	0.00%	0.10%
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent	0.00%	0.30%	1.70%
Effective Income Tax Rate Reconciliation, Change in Enacted Tax Rate, Percent	0.00%	0.00%	(2.00%)
Effective Income Tax Rate Reconciliation, Audits and Adjustments	0.30%	0.40%	(2.90%)
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Research and Development, Percent	(0.40%)	(0.60%)	(0.70%)
Other items	0.50%	(0.40%)	0.70%
Effective income tax rate	23.20%	22.10%	22.10%
Impairment and divestiture (benefit) charges	$ 0	$ 147	$ (6,155)
Effective Income Tax Rate Reconciliation, Withholding Tax, Foreign, Amount	3,000	$ 3,400	2,600
Effective Income Tax Rate Reconciliation audits and adjustments, amount	$ 400		$ 2,000