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Goodwill and Intangible Assets - Intangible Table by Major Class (Details) - USD ($)
$ in Thousands
Feb. 28, 2026
Aug. 31, 2025
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount $ 4,577,580 $ 4,269,992
Accumulated Amortization (2,029,046) (1,859,237)
Net Carrying Amount 2,548,534 2,410,755
Customer-related    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 4,045,034 3,735,706
Accumulated Amortization (1,728,174) (1,572,270)
Net Carrying Amount 2,316,860 2,163,436
Technology    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 294,123 294,292
Accumulated Amortization (186,720) (173,864)
Net Carrying Amount 107,403 120,428
Patents    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 110,668 114,739
Accumulated Amortization (71,006) (72,430)
Net Carrying Amount 39,662 42,309
Other    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Amount 127,755 125,255
Accumulated Amortization (43,146) (40,673)
Net Carrying Amount $ 84,609 $ 84,582