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Goodwill and Intangible Assets - Intangible Table by Major Class (Details) - USD ($)
$ in Thousands
May 31, 2025
Aug. 31, 2024
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount $ 4,469,312 $ 4,530,739
Accumulated Amortization (1,877,627) (1,626,708)
Net Carrying Amount 2,591,685 2,904,031
Customer-related    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 3,884,301 3,924,339
Accumulated Amortization (1,549,918) (1,336,679)
Net Carrying Amount 2,334,383 2,587,660
Technology    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 347,369 335,845
Accumulated Amortization (220,185) (183,182)
Net Carrying Amount 127,184 152,663
Patents    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 115,644 120,457
Accumulated Amortization (72,757) (72,518)
Net Carrying Amount 42,887 47,939
Other    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 121,998 150,098
Accumulated Amortization (34,767) (34,329)
Net Carrying Amount $ 87,231 $ 115,769