Income Taxes - Reconciliation of the Statutory Tax Rates to the Effective Tax Rates (Details)	12 Months Ended
	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Statutory federal income tax rate	21.00%	21.00%	21.00%
State and local income taxes, net of federal income tax benefit	2.40%	0.50%	1.10%
Patronage earnings	(7.80%)	(12.60%)	(13.00%)
Effective Income Tax Rate Reconciliation, Deduction, Percent	(12.90%)	(6.80%)	(3.20%)
Export activities at rates other than the U.S. statutory rate	(3.30%)	1.40%	(0.20%)
Increase in unrecognized tax benefits	2.80%	2.70%	0.00%
Valuation allowance	2.80%	(0.10%)	0.00%
Effective Income Tax Rate Reconciliation, Tax Credit, Percent	(4.30%)	(6.20%)	0.00%
Other	2.00%	(0.30%)	(0.30%)
Effective tax rate	2.70%	0.40%	5.40%