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Common Stock and Related Matters - Earnings per Share (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Earnings per share      
Net income $ 346.0 $ 384.0 $ 306.3
Basic weighted average shares outstanding (in shares) 31,806 34,182 36,284
Common stock equivalents (in shares) 358 463 270
Diluted weighted average number of shares outstanding (in shares) 32,164 34,645 36,554
Basic earnings per share (in dollars per share) [1] $ 10.88 $ 11.23 $ 8.44
Diluted earnings per share (in dollars per share) [1] $ 10.76 $ 11.08 $ 8.38
Stock options      
Earnings per share      
Stock options (less than) excluded from diluted earnings per share (in shares) 100 100 800
Restricted stock awards and units      
Earnings per share      
Stock options (less than) excluded from diluted earnings per share (in shares) 100 100 100
Performance stock units      
Earnings per share      
Stock options (less than) excluded from diluted earnings per share (in shares) 100 0 0
[1] (1) Earnings per share is calculated using unrounded numbers. Amounts in the table may not recalculate exactly due to rounding.