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Income Taxes - Narrative (Details) - USD ($)
$ in Thousands
 12 Months Ended
Aug. 31, 2024
Aug. 31, 2023
Aug. 31, 2022
Income Tax [Line Items]      
Operating loss carryforwards $ 6,300    
Net deferred tax asset 400    
Tax credit carryforwards 4,197 $ 3,918  
Valuation allowance $ 4,305 $ 3,960  
Provision for income taxes 23.90% 22.50%  
Unrecognized tax benefits $ 9,147 $ 9,275 $ 9,251
Unrecognized tax benefits that would impact the effective tax rate 9,000 9,100  
Interest and penalties included in income tax expense 1,200 1,800  
Accrued interest and penalties related to uncertain tax positions 4,600 3,400  
Total unrecognized tax benefits including interest 13,700 12,700  
Unrecognized tax benefits, amount that may be affected within next twelve months 13,100    
Tax Cuts and Jobs Act, toll tax for accumulated foreign earnings 12,700    
Income taxes receivable 500 $ 1,100  
Foreign Tax Jurisdiction      
Income Tax [Line Items]      
Tax credit carryforwards 4,100    
Net increase in its valuation allowance 300    
Valuation allowance 3,900    
State and Local Jurisdiction      
Income Tax [Line Items]      
Valuation allowance $ 400