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Goodwill and Other Intangible Assets (Tables)
 12 Months Ended
Jan. 02, 2021
Goodwill and Intangible Assets Disclosure [Abstract]  
Changes in Carrying Amount of Goodwill by Segment
The changes in the carrying amount of goodwill by segment for 2020 and 2019 are as follows: 
(Amounts in millions)Commercial
& Industrial
Group		Snap-on
Tools Group		Repair Systems 
& Information
Group		Total
Balance as of 2018 year end
$286.2 $12.5 $603.5 $902.2 
Currency translation(6.4)— (1.1)(7.5)
Acquisitions6.4 — 12.7 19.1 
Balance as of 2019 year end$286.2 $12.5 $615.1 $913.8 
Currency translation26.7 (0.1)15.0 41.6 
Acquisitions18.3 — 8.7 27.0 
Balance as of 2020 year end$331.2 $12.4 $638.8 $982.4 
Other Intangible Assets by Major Class
Additional disclosures related to other intangible assets as of 2020 and 2019 year end are as follows: 
 20202019
(Amounts in millions)Gross
Carrying Value		Accumulated
Amortization		Gross
Carrying Value		Accumulated
Amortization
Amortized other intangible assets:
Customer relationships$191.5 $(130.1)$182.9 $(117.9)
Developed technology21.8 (19.9)19.8 (18.9)
Internally developed software172.2 (128.0)168.0 (125.4)
Patents43.2 (25.3)38.5 (23.7)
Trademarks3.9 (2.4)3.5 (2.1)
Other8.2 (3.9)7.3 (3.1)
Total440.8 (309.6)420.0 (291.1)
Non-amortized trademarks129.6 — 115.0 — 
Total other intangible assets$570.4 $(309.6)$535.0 $(291.1)
Weighted-Average Amortization Period by Major Class
The weighted-average amortization periods related to other intangible assets are as follows: 
   In Years
Customer relationships  15
Developed technology  3
Internally developed software  6
Patents  7
Trademarks  5
Other  39