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CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2023
Nov. 30, 2022
Cash flows from operating activities:    
Net income $ 100.6 $ 74.9
Adjustments to reconcile net income to cash flows from operating activities:    
Depreciation and amortization 22.7 26.5
Share-based payment expense 11.1 10.7
Loss on sale of property, plant, and equipment 0.4 0.0
Asset impairment 0.0 4.3
Loss on sale of a business 0.0 11.2
Changes in operating assets and liabilities, net of acquisitions and divestitures:    
Accounts receivable 37.8 81.6
Inventories 3.2 (5.8)
Prepayments and other current assets (5.3) (8.5)
Accounts payable 28.7 20.3
Other operating activities (9.2) (28.6)
Net cash provided by operating activities 190.0 186.6
Cash flows from investing activities:    
Purchases of property, plant, and equipment (14.6) (18.2)
Other investing activities 0.1 3.9
Net cash used for investing activities (14.5) (14.3)
Cash flows from financing activities:    
Repayments on credit facility, net of borrowings 0.0 (18.0)
Repurchases of common stock (48.2) (76.5)
Proceeds from stock option exercises and other 1.6 0.9
Payments of taxes withheld on net settlement of equity awards (9.0) (12.5)
Dividends paid (4.1) (4.3)
Net cash used for financing activities (59.7) (110.4)
Effect of exchange rate changes on cash and cash equivalents (0.4) (1.0)
Net change in cash and cash equivalents 115.4 60.9
Cash and cash equivalents at beginning of period 397.9 223.2
Cash and cash equivalents at end of period 513.3 284.1
Supplemental cash flow information:    
Income taxes paid during the period 7.1 11.0
Interest paid during the period $ 12.8 $ 15.3