Earnings before Income Taxes, Including both Continuing and Discontinued Operations (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Income Tax Disclosure [Abstract]
Income (Loss) from Continuing Operations before Income Taxes, Domestic	$ 59,688	$ 26,442	$ 10,176
Income (Loss) from Continuing Operations before Income Taxes, Foreign	45,831	42,456	13,816
Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest	$ 105,519	$ 68,898	$ 23,992