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Changes in Stockholders' Equity (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
 3 Months Ended 9 Months Ended
May 31, 2024
Feb. 29, 2024
Nov. 30, 2023
May 31, 2023
Feb. 28, 2023
Nov. 30, 2022
May 31, 2024
May 31, 2023
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance $ 2,149.6 $ 2,064.1 $ 2,015.4 $ 1,947.6 $ 1,903.5 $ 1,911.8 $ 2,015.4 $ 1,911.8
Net income 113.9 89.2 100.6 105.0 83.2 74.9 303.7 263.1
Other comprehensive (loss) income 0.8 1.4 (1.5) 6.3 (0.1) (0.4)    
Share-based payment amortization, issuances, and cancellations 10.7 11.8 2.1 9.4 10.9 (1.8)    
Employee stock purchase plan issuances 0.4 0.3 0.5 0.4 0.3 0.5    
Cash dividends paid on common stock (4.6) (4.7) (4.1) (4.2) (4.2) (4.3)    
Stock options exercised 4.6 5.1 1.1   0.5 0.4    
Repurchases of common stock (20.7) (17.6) (50.0) (94.7) (46.5) (77.6)    
Ending balance $ 2,254.7 $ 2,149.6 $ 2,064.1 $ 1,969.8 $ 1,947.6 $ 1,903.5 $ 2,254.7 $ 1,969.8
Cash dividends paid (in usd per share) $ 0.15 $ 0.15 $ 0.13 $ 0.13 $ 0.13 $ 0.13    
Common Stock Outstanding                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance (in shares) 30.8 30.9 31.1 32.0 32.2 32.5 31.1 32.5
Beginning balance $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5
Share-based payment amortization, issuances, and cancellations (in shares)     0.1     0.2    
Repurchases of common stock (in shares) (0.1) (0.1) (0.3) (0.6) (0.2) (0.5)    
Ending balance (in shares) 30.7 30.8 30.9 31.4 32.0 32.2 30.7 31.4
Ending balance $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5
Paid-in Capital                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance 1,087.7 1,070.5 1,066.8 1,047.1 1,035.4 1,036.3 1,066.8 1,036.3
Share-based payment amortization, issuances, and cancellations 10.7 11.8 2.1 9.4 10.9 (1.8)    
Employee stock purchase plan issuances 0.4 0.3 0.5 0.4 0.3 0.5    
Stock options exercised 4.6 5.1 1.1   0.5 0.4    
Ending balance 1,103.4 1,087.7 1,070.5 1,056.9 1,047.1 1,035.4 1,103.4 1,056.9
Retained Earnings                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance 3,686.4 3,601.9 3,505.4 3,325.8 3,246.8 3,176.2 3,505.4 3,176.2
Net income 113.9 89.2 100.6 105.0 83.2 74.9    
Cash dividends paid on common stock (4.6) (4.7) (4.1) (4.2) (4.2) (4.3)    
Ending balance 3,795.7 3,686.4 3,601.9 3,426.6 3,325.8 3,246.8 3,795.7 3,426.6
Accumulated Other Comprehensive Loss                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance (112.7) (114.1) (112.6) (126.3) (126.2) (125.8) (112.6) (125.8)
Other comprehensive (loss) income 0.8 1.4 (1.5) 6.3 (0.1) (0.4)    
Ending balance (111.9) (112.7) (114.1) (120.0) (126.3) (126.2) (111.9) (120.0)
Treasury Stock, at cost                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance (2,512.3) (2,494.7) (2,444.7) (2,299.5) (2,253.0) (2,175.4) (2,444.7) (2,175.4)
Repurchases of common stock (20.7) (17.6) (50.0) (94.7) (46.5) (77.6)    
Ending balance $ (2,533.0) $ (2,512.3) $ (2,494.7) $ (2,394.2) $ (2,299.5) $ (2,253.0) $ (2,533.0) $ (2,394.2)