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Earnings Per Share - Schedule of Basic and Diluted Earnings Per Share (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Thousands
3 Months Ended
Nov. 26, 2021
Nov. 27, 2020
Earnings Per Share [Abstract]    
Net income attributable to SGH – Basic and Diluted $ 20,027 $ 2,027
Weighted-average shares outstanding – Basic 24,506 24,561
Dilutive effect of equity plans and convertible notes 2,812 542
Weighted-average shares outstanding – Diluted 27,318 25,103
Earnings per share:    
Basic $ 0.82 $ 0.08
Diluted $ 0.73 $ 0.08