Intangible assets - Finite-Lived and Indefinite-Lived Intangible Assets (Details) - USD ($) $ in Millions	Mar. 29, 2025	Dec. 28, 2024
Finite-Lived Intangible Assets
Finite-lived, cost	$ 2,177.9	$ 2,150.2
Finite-lived, accumulated amortization and impairment	(1,414.8)	(1,371.0)
Finite-lived, net	763.1	779.2
Indefinite-lived, cost	513.4	513.4
Indefinite-lived, accumulated amortization and impairment	(44.0)	(44.0)
Indefinite-lived, net	469.4	469.4
Cost	2,691.3	2,663.6
Accumulated amortization and impairment	(1,458.8)	(1,415.0)
Net	1,232.5	1,248.6
—Customer relationships
Finite-Lived Intangible Assets
Finite-lived, cost	1,939.0	1,921.5
Finite-lived, accumulated amortization and impairment	(1,234.8)	(1,194.7)
Finite-lived, net	704.2	726.8
—Technology
Finite-Lived Intangible Assets
Finite-lived, cost	90.6	90.5
Finite-lived, accumulated amortization and impairment	(90.6)	(90.5)
Finite-lived, net	0.0	0.0
—Capitalized software
Finite-Lived Intangible Assets
Finite-lived, cost	148.3	138.2
Finite-lived, accumulated amortization and impairment	(89.4)	(85.8)
Finite-lived, net	$ 58.9	$ 52.4

Indefinite-Lived Intangible Assets (Excluding Goodwill), Gross

No definition available.

Name:	gtes_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross
Namespace Prefix:	gtes_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Indefinite-Lived Intangible Assets (Excluding Goodwill), Impaired, Accumulated Impairment Loss

+ References

No definition available.

+ Details

Name:	gtes_IndefiniteLivedIntangibleAssetsExcludingGoodwillImpairedAccumulatedImpairmentLoss
Namespace Prefix:	gtes_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Intangible Assets (Excluding Goodwill), Accumulated Amortization and Impairment Loss

+ References

No definition available.

+ Details

Name:	gtes_IntangibleAssetsExcludingGoodwillAccumulatedAmortizationAndImpairmentLoss
Namespace Prefix:	gtes_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

+ References

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount before amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

+ References

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 55
-Paragraph 40
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482640/350-30-55-40

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (d)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482665/350-30-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (d)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482665/350-30-50-2

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482686/350-30-45-1

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482665/350-30-50-2

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482665/350-30-50-3

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 985
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481283/985-20-50-2

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Topic 926
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483154/926-20-50-5

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount after amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

+ References

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of assets, excluding financial assets and goodwill, lacking physical substance and having a projected indefinite period of benefit.

+ References

+ Details

Name:	us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount before accumulated amortization of intangible assets, excluding goodwill.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(15))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_IntangibleAssetsGrossExcludingGoodwill
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Sum of the carrying amounts of all intangible assets, excluding goodwill, as of the balance sheet date, net of accumulated amortization and impairment charges.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482665/350-30-50-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482665/350-30-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482686/350-30-45-1

+ Details

Name:	us-gaap_IntangibleAssetsNetExcludingGoodwill
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_CustomerRelationshipsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_TechnologyBasedIntangibleAssetsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_ComputerSoftwareIntangibleAssetMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: