Accounts receivable, net - Credit Quality Indicator and Age Analysis (Details) - USD ($) $ in Millions	Jul. 29, 2017	Jan. 28, 2017	Jul. 30, 2016
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 1,792.5	$ 1,952.0	$ 1,745.0
Valuation allowance	$ (135.0)	$ (138.7)	$ (129.4)
Gross	100.00%	100.00%	100.00%
Valuation allowance	7.50%	7.10%	7.40%
Gross	$ 1,055.6	$ 0.0	$ 0.0
Valuation allowance	(20.7)	0.0	0.0
Gross	736.9	1,952.0	1,745.0
Valuation allowance	(114.3)	(138.7)	(129.4)
Current, aged 0 – 30 days | Performing Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	1,394.2	1,538.2	1,350.7
Valuation allowance	$ (42.8)	$ (47.2)	$ (41.3)
Gross	77.80%	78.80%	77.40%
Valuation allowance	3.10%	3.10%	3.10%
Past due, aged 31 – 60 days | Performing Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 264.6	$ 282.0	$ 264.1
Valuation allowance	$ (8.6)	$ (9.0)	$ (8.6)
Gross	14.80%	14.50%	15.10%
Valuation allowance	3.30%	3.20%	3.30%
Past due, aged 61 – 90 days | Performing Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 52.5	$ 51.6	$ 53.2
Valuation allowance	$ (2.4)	$ (2.3)	$ (2.5)
Gross	2.90%	2.60%	3.10%
Valuation allowance	4.60%	4.50%	4.70%
Past due, aged more than 90 days | Nonperforming Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 81.2	$ 80.2	$ 77.0
Valuation allowance	$ (81.2)	$ (80.2)	$ (77.0)
Gross	4.50%	4.10%	4.40%
Valuation allowance	100.00%	100.00%	100.00%