Condensed Consolidated Statements of Shareholder's Equity - USD ($) shares in Millions, $ in Millions	Total	Open Market Purchases And Private Purchases	Open Market Purchases	ASR	Cumulative Effect, Period of Adoption, Adjustment	Total Shareholders' Equity	Total Shareholders' Equity Open Market Purchases And Private Purchases	Total Shareholders' Equity Open Market Purchases	Total Shareholders' Equity ASR	Common Stock	Common Stock Open Market Purchases And Private Purchases	Common Stock Open Market Purchases	Common Stock ASR	Additional Paid-in Capital	Additional Paid-in Capital ASR	Accumulated Earnings (Defecit)	Accumulated Earnings (Defecit) Cumulative Effect, Period of Adoption, Adjustment	Accumulated Other Comprehensive Loss	Accumulated Other Comprehensive Loss Cumulative Effect, Period of Adoption, Adjustment	Treasury Stock	Treasury Stock Open Market Purchases And Private Purchases	Treasury Stock Open Market Purchases	Treasury Stock ASR	Non- controlling Interest	SB/RH	SB/RH Cumulative Effect, Period of Adoption, Adjustment	SB/RH Total Shareholders' Equity	SB/RH Other Capital	SB/RH Accumulated Earnings (Defecit)	SB/RH Accumulated Earnings (Defecit) Cumulative Effect, Period of Adoption, Adjustment	SB/RH Accumulated Other Comprehensive Loss	SB/RH Accumulated Other Comprehensive Loss Cumulative Effect, Period of Adoption, Adjustment	SB/RH Non- controlling Interest
Balances at beginning of period (in shares) at Sep. 30, 2019										48.8
Balances at beginning of period at Sep. 30, 2019	$ 1,728.9				$ 0.0	$ 1,720.9				$ 0.5				$ 2,031.1		$ 223.8	$ (0.3)	$ (273.6)	$ 0.3	$ (260.9)				$ 8.0	$ 1,434.7	$ 0.0	$ 1,425.1	$ 2,113.3	$ (414.7)	$ (0.3)	$ (273.5)	$ 0.3	$ 9.6
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) from continuing operations	(37.7)					(38.6)										(38.6)								0.9	(36.8)		(37.7)		(37.7)				0.9
Income (loss) from discontinued operations, net of tax	2.8					2.8										2.8									2.8		2.8		2.8
Other comprehensive income (loss), net of tax	24.3					24.2												24.2						0.1	24.3		24.2				24.2		0.1
Treasury stock repurchases (in shares)											(1.5)		(1.7)
Treasury stock repurchases		$ (90.6)		$ (125.0)			$ (90.6)		$ (125.0)						$ (18.7)						$ (90.6)		$ (106.3)
Restricted stock issued and related tax withholdings (in shares)										0.5
Restricted stock issued and related tax withholdings	4.9					4.9								(13.3)						18.2					4.9		4.9	4.9
Share based compensation	8.5					8.5								8.5											8.5		8.5	8.5
Dividends paid to parent																									(36.7)		(36.7)		(36.7)
Dividends declared	(20.2)					(20.2)										(20.2)
Balances at end of period (in shares) at Dec. 29, 2019										46.1
Balances at end of period at Dec. 29, 2019	1,495.9					1,486.9				$ 0.5				2,007.6		167.5		(249.1)		(439.6)				9.0	1,401.7		1,391.1	2,126.7	(486.6)		(249.0)		10.6
Balances at beginning of period (in shares) at Sep. 30, 2019										48.8
Balances at beginning of period at Sep. 30, 2019	1,728.9				0.0	1,720.9				$ 0.5				2,031.1		223.8	(0.3)	(273.6)	0.3	(260.9)				8.0	1,434.7	0.0	1,425.1	2,113.3	(414.7)	(0.3)	(273.5)	0.3	9.6
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) from continuing operations	40.8																								(12.2)
Income (loss) from discontinued operations, net of tax	$ 12.2																								12.2
Treasury stock repurchases (in shares)	(6.2)		(4.0)	(2.0)
Treasury stock repurchases																				(364.6)		$ (230.6)	(124.8)
Balances at end of period (in shares) at Jun. 28, 2020										43.1
Balances at end of period at Jun. 28, 2020	$ 1,385.5					1,376.9				$ 0.5				2,042.8		217.3		(276.8)		(606.9)				8.6	1,237.9		1,227.7	2,142.9	(638.5)		(276.7)		10.2
Balances at beginning of period (in shares) at Sep. 30, 2019										48.8
Balances at beginning of period at Sep. 30, 2019	1,728.9				$ 0.0	1,720.9				$ 0.5				2,031.1		223.8	$ (0.3)	(273.6)	$ 0.3	(260.9)				8.0	1,434.7	$ 0.0	1,425.1	2,113.3	(414.7)	$ (0.3)	(273.5)	$ 0.3	9.6
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Treasury stock repurchases (in shares)				(2.0)
Balances at end of period (in shares) at Sep. 30, 2020										43.1
Balances at end of period at Sep. 30, 2020	1,415.8					1,407.5				$ 0.5				2,054.3		243.9		(284.7)		(606.5)				8.3	1,265.2		1,255.3	2,154.1	(614.2)		(284.6)		9.9
Balances at beginning of period (in shares) at Dec. 29, 2019										46.1
Balances at beginning of period at Dec. 29, 2019	1,495.9					1,486.9				$ 0.5				2,007.6		167.5		(249.1)		(439.6)				9.0	1,401.7		1,391.1	2,126.7	(486.6)		(249.0)		10.6
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) from continuing operations	(59.2)					(58.4)										(58.4)								(0.8)	(56.6)		(55.8)		(55.8)				(0.8)
Income (loss) from discontinued operations, net of tax	1.4					1.4										1.4											1.4		1.4
Sale and deconsolidation of assets held for sale	8.1					8.1												8.1							8.1		8.1				8.1
Other comprehensive income (loss), net of tax	(41.1)					(41.0)												(41.0)						(0.1)	(41.1)		(41.0)				(41.0)		(0.1)
Treasury stock repurchases (in shares)												(2.7)	(0.3)
Treasury stock repurchases			$ (149.2)	$ 0.0				$ (149.2)							$ 18.5							(149.2)	(18.5)
Restricted stock issued and related tax withholdings	(0.3)					(0.3)								(0.7)						0.4					(0.3)		(0.3)	(0.3)
Share based compensation	8.9					8.9								8.9											8.3		8.3	8.3
Dividends paid to parent																									(168.2)		(168.2)		(168.2)
Dividends declared	(19.7)					(19.7)										(19.7)
Balances at end of period (in shares) at Mar. 29, 2020										43.1
Balances at end of period at Mar. 29, 2020	1,244.8					1,236.7				$ 0.5				2,034.3		90.8		(282.0)		(606.9)				8.1	1,153.3		1,143.6	2,134.7	(709.2)		(281.9)		9.7
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) from continuing operations	137.6					137.1										137.1								0.5	81.3		80.8		80.8				0.5
Income (loss) from discontinued operations, net of tax	8.0					8.0										8.0									8.0		8.0		8.0
Other comprehensive income (loss), net of tax	$ 5.2					5.2												5.2							5.2		5.2				5.2
Treasury stock repurchases (in shares)	0.0		0.0
Treasury stock repurchases																				0.0		0.0
Restricted stock issued and related tax withholdings	$ (0.1)					(0.1)								(0.1)
Share based compensation	8.6					8.6								8.6											8.2		8.2	8.2
Dividends paid to parent																									(18.1)		(18.1)		(18.1)
Dividends declared	(18.6)					(18.6)										(18.6)
Balances at end of period (in shares) at Jun. 28, 2020										43.1
Balances at end of period at Jun. 28, 2020	1,385.5					1,376.9				$ 0.5				2,042.8		217.3		(276.8)		(606.9)				8.6	1,237.9		1,227.7	2,142.9	(638.5)		(276.7)		10.2
Balances at beginning of period (in shares) at Sep. 30, 2020										43.1
Balances at beginning of period at Sep. 30, 2020	1,415.8					1,407.5				$ 0.5				2,054.3		243.9		(284.7)		(606.5)				8.3	1,265.2		1,255.3	2,154.1	(614.2)		(284.6)		9.9
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) from continuing operations	73.2					72.4										72.4								0.8	73.6		72.8		72.8				0.8
Income (loss) from discontinued operations, net of tax	(0.3)					(0.3)										(0.3)									(0.3)		(0.3)		(0.3)
Other comprehensive income (loss), net of tax	16.6					16.2												16.2						0.4	16.6		16.2				16.2		0.4
Treasury stock repurchases (in shares)										(0.6)
Treasury stock repurchases	(42.3)					(42.3)														(42.3)
Restricted stock issued and related tax withholdings (in shares)										0.2
Restricted stock issued and related tax withholdings	(6.9)					(6.9)								(18.6)						11.7					(7.1)		(7.1)	(7.1)
Share based compensation	7.5					7.5								7.5											7.5		7.5	7.5
Dividends paid to parent																									(60.1)		(60.1)		(60.1)
Dividends declared	(18.4)					(18.4)										(18.4)
Dividend paid by subsidiary to NCI	(1.0)																							(1.0)	(1.0)								(1.0)
Balances at end of period (in shares) at Jan. 03, 2021										42.7
Balances at end of period at Jan. 03, 2021	1,444.2					1,435.7				$ 0.5				2,043.2		297.6		(268.5)		(637.1)				8.5	1,294.4		1,284.3	2,154.5	(601.8)		(268.4)		10.1
Balances at beginning of period (in shares) at Sep. 30, 2020										43.1
Balances at beginning of period at Sep. 30, 2020	1,415.8					1,407.5				$ 0.5				2,054.3		243.9		(284.7)		(606.5)				8.3	1,265.2		1,255.3	2,154.1	(614.2)		(284.6)		9.9
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) from continuing operations	145.9																								147.9
Income (loss) from discontinued operations, net of tax	$ (6.6)																								(6.6)
Treasury stock repurchases (in shares)	(0.7)		(0.1)	0.0
Treasury stock repurchases																				(52.5)		(10.2)	$ 0.0
Balances at end of period (in shares) at Jul. 04, 2021										42.6
Balances at end of period at Jul. 04, 2021	$ 1,508.2					1,500.9				$ 0.5				2,058.0		328.1		(239.6)		(646.1)				7.3	1,361.6		1,352.7	2,169.4	(577.2)		(239.5)		8.9
Balances at beginning of period (in shares) at Jan. 03, 2021										42.7
Balances at beginning of period at Jan. 03, 2021	1,444.2					1,435.7				$ 0.5				2,043.2		297.6		(268.5)		(637.1)				8.5	1,294.4		1,284.3	2,154.5	(601.8)		(268.4)		10.1
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) from continuing operations	36.8					37.7										37.7								(0.9)	37.3		38.2		38.2				(0.9)
Income (loss) from discontinued operations, net of tax	(1.1)					(1.1)										(1.1)									(1.1)		(1.1)		(1.1)
Sale and deconsolidation of assets held for sale	0.0
Other comprehensive income (loss), net of tax	25.0					25.1												25.1						(0.1)	25.0		25.1				25.1		(0.1)
Restricted stock issued and related tax withholdings	0.0													(0.1)						0.1
Share based compensation	8.5					8.5								8.5											8.0		8.0	8.0
Dividends paid to parent																									(16.1)		(16.1)		(16.1)
Dividends declared	(18.5)					(18.5)										(18.5)
Dividend paid by subsidiary to NCI	(0.3)																							(0.3)	(0.3)								(0.3)
Balances at end of period (in shares) at Apr. 04, 2021										42.7
Balances at end of period at Apr. 04, 2021	1,494.6					1,487.4				$ 0.5				2,051.6		315.7		(243.4)		(637.0)				7.2	1,347.2		1,338.4	2,162.5	(580.8)		(243.3)		8.8
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) from continuing operations	35.9					35.9										35.9									36.9		36.9		36.9
Income (loss) from discontinued operations, net of tax	(5.2)					(5.2)										(5.2)									(5.2)		(5.2)		(5.2)
Other comprehensive income (loss), net of tax	$ 3.9					3.8												3.8						0.1	3.9		3.8				3.8		0.1
Treasury stock repurchases (in shares)	(0.1)		(0.1)								(0.1)
Treasury stock repurchases		$ (10.2)					$ (10.2)													(10.2)	$ (10.2)	$ (10.2)
Restricted stock issued and related tax withholdings	$ 0.0													(1.1)						1.1
Share based compensation	7.5					7.5								7.5											6.9		6.9	6.9
Dividends paid to parent																									(28.1)		(28.1)		(28.1)
Dividends declared	(18.3)					(18.3)										(18.3)
Balances at end of period (in shares) at Jul. 04, 2021										42.6
Balances at end of period at Jul. 04, 2021	$ 1,508.2					$ 1,500.9				$ 0.5				$ 2,058.0		$ 328.1		$ (239.6)		$ (646.1)				$ 7.3	$ 1,361.6		$ 1,352.7	$ 2,169.4	$ (577.2)		$ (239.5)		$ 8.9