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Income Taxes - Reconciliation of the Statutory Tax Rates to the Effective Tax Rates (Details)	12 Months Ended
	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
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	0.50%	1.10%	1.10%
Patronage earnings	(12.60%)	(13.00%)	(13.60%)
Effective Income Tax Rate Reconciliation, Deduction, Percent	(6.80%)	(3.20%)	(3.20%)
Export activities at rates other than the U.S. statutory rate	1.40%	(0.20%)	0.40%
Intercompany transfer of business assets	0.00%	0.00%	(0.10%)
Increase in unrecognized tax benefits	2.70%	0.00%	0.00%
Valuation allowance	(0.10%)	0.00%	0.20%
Effective Income Tax Rate Reconciliation, Tax Credit, Percent	(6.20%)	0.00%	0.00%
Other	(0.30%)	(0.30%)	1.50%
Effective tax rate	(0.40%)	(5.40%)	(7.30%)

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Effective Income Tax Rate, Rate Reconciliation, Patronage Earnings

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Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

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Percentage of domestic federal statutory tax rate applicable to pretax income (loss).

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Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to changes in the valuation allowance for deferred tax assets.

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Percentage of difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying domestic federal statutory income tax rate to pretax income (loss) from continuing operations attributable to deduction. Includes, but is not limited to, dividend deduction, deduction for dividend paid to employee stock ownership plan (ESOP), Medicare prescription drug benefit subsidy deduction, and other deductions.

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Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to tax credits. Including, but not limited to, research credit, foreign tax credit, investment tax credit, and other tax credits.

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