Income Taxes - Reconciliation of the Statutory Tax Rates to the Effective Tax Rates (Details)	12 Months Ended
Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
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	1.10%	1.10%	(2.60%)
Patronage earnings	(13.00%)	(13.60%)	(11.40%)
Effective Income Tax Rate Reconciliation, Deduction, Percent	(3.20%)	(3.20%)	(8.20%)
Export activities at rates other than the U.S. statutory rate	(0.20%)	0.40%	0.50%
Intercompany transfer of business assets	0.00%	(0.10%)	(4.70%)
Increase in unrecognized tax benefits	0.00%	0.00%	0.80%
Valuation allowance	0.00%	0.20%	(0.20%)
Other	(0.30%)	1.50%	(2.60%)
Effective tax rate	5.40%	7.30%	(7.40%)

Effective Income Tax Rate, Rate Reconciliation, Patronage Earnings

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- Definition

Effective Income Tax Rate Reconciliation, Change In Unrecognized Tax Benefits

+ References

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- Definition

Effective Income Tax Rate Reconciliation, Intercompany Transfer Of Assets

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- Definition

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

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

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- Definition

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

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480678/235-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479360/740-10-S99-1

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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.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479360/740-10-S99-1

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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 applicable to statutory income tax expense (benefit) outside of the country of domicile.

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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 applicable to state and local income tax expense (benefit), net of federal tax expense (benefit).

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