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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, 2025
Aug. 31, 2024
Aug. 31, 2023
Equity [Abstract]      
Net income $ 396.6 $ 422.6 $ 346.0
Basic weighted average shares outstanding (in shares) [1] 30,859 30,885 31,806
Common stock equivalents (in shares) 782 560 358
Diluted weighted average number of shares outstanding (in shares) [1] 31,641 31,445 32,164
Basic earnings per share (in dollars per share) [1] $ 12.85 $ 13.68 $ 10.88
Diluted earnings per share (in dollars per share) [1] $ 12.53 $ 13.44 $ 10.76
[1] Earnings per share is calculated using unrounded numbers. Amounts in the table may not recalculate exactly due to rounding.