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Share-Based Compensation (Details 3) (USD $)
In Millions, unless otherwise specified
 3 Months Ended
Apr. 04, 2015
Mar. 29, 2014
Restricted Stock Units    
Share-Based Compensation    
Fair value of awards vested $ 22us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember		 $ 20us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
Cash paid 18txt_IntrinsicValueOfCashAwardsPaid
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember		 19txt_IntrinsicValueOfCashAwardsPaid
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
Performance Share Units    
Share-Based Compensation    
Cash paid $ 17txt_IntrinsicValueOfCashAwardsPaid
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember		 $ 12txt_IntrinsicValueOfCashAwardsPaid
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember