This work demostrate the equivalence of the following definitions "let 1 ≤ p ≤ ∞, be, φ ε L(X1, ⋯p ,Xn; Y ) is called p-factorable, if exist a measure space (ω,σ, μ) and operators A ε L(Lp(μ), Y **) and φ ε L(X1, ⋯ ,Xn;Lp(μ)) such that KY o φ = A o φ. The collection of the p-factorable multi-linear operators of X1, ⋯ ,Xn to Y will be denoted for Lp-fact(X1, ⋯ ,Xn, Y ). Also γp(φ) = inf || φ || || A||, where the infimun is taken over all possible factorzation of φ is a norm over Lp-fact(X1, ⋯, Xn; Y )" and "let 1 ≤ p ≤ 8. A operator φ ε L(E1, ⋯ ,En; F) is called p-factorable relative to (q1, ⋯ , qn) if belongs to the normed ideal. © 2013 Academic Publications, Ltd.