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Changes in Stockholders' Equity (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
 3 Months Ended 6 Months Ended
Feb. 28, 2022
Nov. 30, 2021
Feb. 28, 2021
Nov. 30, 2020
Feb. 28, 2022
Feb. 28, 2021
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Beginning balance $ 2,072.9 $ 2,044.5 $ 1,937.0 $ 2,127.5 $ 2,044.5 $ 2,127.5
Net income 75.3 87.6 62.9 59.6 162.9 122.5
Other comprehensive income (loss) 6.0 (10.7) 8.4 6.2 (4.7) 14.6
Share-based payment amortization, issuances, and cancellations 9.4 0.4 8.6 4.7    
Employee stock purchase plan issuances 0.4 0.6 0.2 0.3    
Cash dividends of $0.13 per share paid on common stock (4.6) (4.7) (4.7) (5.0)    
Stock options exercised 1.2 8.0 0.4      
Repurchases of common stock (56.3) (52.8) (80.3) (256.1)    
Ending balance $ 2,104.3 $ 2,072.9 $ 1,932.5 $ 1,937.0 2,104.3 1,932.5
Cash dividends paid (usd per share) $ 0.13 $ 0.13 $ 0.13 $ 0.13    
Common Stock Outstanding            
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Beginning balance $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5
Beginning balance (shares) 35.1 35.2 36.4 38.9 35.2 38.9
Share-based payment amortization, issuances, and cancellations (shares) 0.0 0.1 0.0 0.1    
Stock options exercised (shares)   0.1        
Repurchases of common stock (shares) (0.3) (0.3) (0.7) (2.6)    
Ending balance $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5
Ending balance (shares) 34.8 35.1 35.7 36.4 34.8 35.7
Paid-in Capital            
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Beginning balance $ 1,004.6 $ 995.6 $ 968.6 $ 963.6 $ 995.6 $ 963.6
Share-based payment amortization, issuances, and cancellations 9.4 0.4 8.6 4.7    
Employee stock purchase plan issuances 0.4 0.6 0.2 0.3    
Stock options exercised 1.2 8.0 0.4      
Ending balance 1,015.6 1,004.6 977.8 968.6 1,015.6 977.8
Retained Earnings            
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Beginning balance 2,893.2 2,810.3 2,577.7 2,523.3 2,810.3 2,523.3
Net income 75.3 87.6 62.9 59.6    
Cash dividends of $0.13 per share paid on common stock (4.6) (4.7) (4.7) (5.0)    
Ending balance 2,963.9 2,893.2 2,635.9 2,577.7 2,963.9 2,635.9
Accumulated Other Comprehensive Loss            
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Beginning balance (108.9) (98.2) (126.5) (132.7) (98.2) (132.7)
Other comprehensive income (loss) 6.0 (10.7) 8.4 6.2    
Ending balance (102.9) (108.9) (118.1) (126.5) (102.9) (118.1)
Treasury Stock, at cost            
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Beginning balance (1,716.5) (1,663.7) (1,483.3) (1,227.2) (1,663.7) (1,227.2)
Repurchases of common stock (56.3) (52.8) (80.3) (256.1)    
Ending balance $ (1,772.8) $ (1,716.5) $ (1,563.6) (1,483.3) $ (1,772.8) (1,563.6)
Cumulative effect of adoption of ASC 326            
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Beginning balance       (0.2)   (0.2)
Cumulative effect of adoption of ASC 326 | Retained Earnings            
Increase (Decrease) in Stockholders' Equity [Roll Forward]            
Beginning balance       $ (0.2)   $ (0.2)