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Other Intangible Assets, Net (Details) - USD ($) $ in Millions | Oct. 31, 2019 | Jan. 31, 2019
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Finite-Lived Intangible Assets [Line Items] |  |
Other intangible assets, at cost | $ 1,178.8 | $ 1,203.3
Less: Accumulated amortization | (953.6) | (922.5)
Other intangible assets, net | 225.2 | 280.8
Developed technologies |  |
Finite-Lived Intangible Assets [Line Items] |  |
Other intangible assets, at cost | 647.0 | 670.2
Customer relationships, trade names, patents, and user lists |  |
Finite-Lived Intangible Assets [Line Items] |  |
Other intangible assets, at cost | $ 531.8 | $ 533.1

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