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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, 2022
Feb. 28, 2022
Nov. 30, 2021
May 31, 2021
Feb. 28, 2021
Nov. 30, 2020
May 31, 2022
May 31, 2021
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance $ 2,104.3 $ 2,072.9 $ 2,044.5 $ 1,932.5 $ 1,937.0 $ 2,127.5 $ 2,044.5 $ 2,127.5
Net income 105.7 75.3 87.6 85.7 62.9 59.6 268.6 208.2
Other comprehensive income (loss) (0.6) 6.0 (10.7) 20.7 8.4 6.2 (5.3) 35.3
Share-based payment amortization, issuances, and cancellations 9.2 9.4 0.4 6.2 8.6 4.7    
Employee stock purchase plan issuances 0.4 0.4 0.6 0.3 0.2 0.3    
Cash dividends of $0.13 per share paid on common stock (4.4) (4.6) (4.7) (4.6) (4.7) (5.0)    
Stock options exercised   1.2 8.0 0.8 0.4      
Repurchases of common stock (296.0) (56.3) (52.8) (2.5) (80.3) (256.1)    
Ending balance $ 1,918.6 $ 2,104.3 $ 2,072.9 $ 2,039.1 $ 1,932.5 $ 1,937.0 $ 1,918.6 $ 2,039.1
Cash dividends paid (usd per share) $ 0.13 $ 0.13 $ 0.13 $ 0.13 $ 0.13 $ 0.13    
Common Stock Outstanding                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance (shares) 34.8 35.1 35.2 35.7 36.4 38.9 35.2 38.9
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 (shares)     0.1 0.0 0.0 0.1    
Stock options exercised (shares)     0.1          
Repurchases of common stock (shares) (1.7) (0.3) (0.3)   (0.7) (2.6)    
Ending balance (shares) 33.1 34.8 35.1 35.7 35.7 36.4 33.1 35.7
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 1,015.6 1,004.6 995.6 977.8 968.6 963.6 995.6 963.6
Share-based payment amortization, issuances, and cancellations 9.2 9.4 0.4 6.2 8.6 4.7    
Employee stock purchase plan issuances 0.4 0.4 0.6 0.3 0.2 0.3    
Stock options exercised   1.2 8.0 0.8 0.4      
Ending balance 1,025.2 1,015.6 1,004.6 985.1 977.8 968.6 1,025.2 985.1
Retained Earnings                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance 2,963.9 2,893.2 2,810.3 2,635.9 2,577.7 2,523.3 2,810.3 2,523.3
Net income 105.7 75.3 87.6 85.7 62.9 59.6    
Cash dividends of $0.13 per share paid on common stock (4.4) (4.6) (4.7) (4.6) (4.7) (5.0)    
Ending balance 3,065.2 2,963.9 2,893.2 2,717.0 2,635.9 2,577.7 3,065.2 2,717.0
Accumulated Other Comprehensive Loss                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance (102.9) (108.9) (98.2) (118.1) (126.5) (132.7) (98.2) (132.7)
Other comprehensive income (loss) (0.6) 6.0 (10.7) 20.7 8.4 6.2    
Ending balance (103.5) (102.9) (108.9) (97.4) (118.1) (126.5) (103.5) (97.4)
Treasury Stock, at cost                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance (1,772.8) (1,716.5) (1,663.7) (1,563.6) (1,483.3) (1,227.2) (1,663.7) (1,227.2)
Repurchases of common stock (296.0) (56.3) (52.8) (2.5) (80.3) (256.1)    
Ending balance $ (2,068.8) $ (1,772.8) $ (1,716.5) $ (1,566.1) $ (1,563.6) (1,483.3) $ (2,068.8) (1,566.1)
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)