Stock-Based Compensation and Shareholders' Equity - Textual (Details) - USD ($)	12 Months Ended
	Oct. 28, 2017	Oct. 29, 2016	Oct. 31, 2015	Oct. 28, 2006
Stock-Based Compensation (Textuals) [Abstract]
Maximum contractual term of all option	10 years
Total number of common shares available for future grantUnits/Awards granted (in shares)	14,700,000.0
Shares reserved for future issuance under 2006 plan	29,700,000.0
Units/Awards granted (USD per share)	$ 79.76
Minimum maturity of traded options used to estimate volatility	1 year
Annual forfeiture rate	4.70%
Total intrinsic value of options exercised	$ 144,600,000	$ 46,600,000	$ 99,200,000
Proceeds (cash) received from exercise of options	133,300,000	61,500,000	122,600,000
Total unrecognized compensation cost related to unvested share-based awards, before tax consideration	$ 375,200,000
Weighted-average period for recognition of compensation cost in years	1 year 11 months
Total grant-date fair value of vested stock options	$ 114,800,000	$ 62,800,000	$ 65,600,000
Preferred stock, shares authorized (in shares)	471,934	471,934
Preferred stock, par value (USD per share)	$ 1	$ 1
Preferred stock, shares outstanding (in shares)	0	0
Preferred stock, shares issued (in share)	0
Employee Stock Option [Member]
Stock-Based Compensation (Textuals) [Abstract]
Percentage of awards exercisable in annual installments on each of the first, second, third, fourth and fifth anniversaries	20.00%
Stock-based compensation awards vesting period (years)	5 years
Restricted Stock Units (RSUs) [Member]
Stock-Based Compensation (Textuals) [Abstract]
Percentage of awards exercisable in annual installments on each of the first, second, third, fourth and fifth anniversaries	20.00%
Stock-based compensation awards vesting period (years)	3 years
2006 Stock Incentive Plan [Member]
Stock-Based Compensation (Textuals) [Abstract]
Maximum common stock granted (in shares)				34,000,000
Share-based compensation arrangement by share-based payment award, terms of award	While the Company may grant to employees options that become exercisable at different times or within different periods, the Company has generally granted to employees options that vest over five years and become exercisable in annual installments of 20% on each of the first, second, third, fourth and fifth anniversaries of the date of grant.
Common Stock Repurchase Program [Member]
Stock-Based Compensation (Textuals) [Abstract]
Amount authorized to repurchase company common stock	$ 6,200,000,000.0
Repurchased common stock, shares (in shares)	147,000,000
Repurchased common stock, value	$ 5,400,000,000
Repurchase of common stock	$ 792,500,000
Linear Technology Corporation [Member]
Stock-Based Compensation (Textuals) [Abstract]
Number of share issued (shares)	2,800,000
Units/Awards granted (USD per share)	$ 82.20