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For two types of moderate growth representations $(\mathbb{R}^d,+)$ on sequentially complete locally convex Hausdorff spaces (including F-representations [J. Funct. Anal. 262 (2012), 667-681], we introduce Denjoy-Carleman classes ultradifferentiable vectors and show a strong factorization theorem Dixmier-Malliavin type for them. In particular, our solves [Conjecture 6.; J. 667-681] analytic $G =(\mathbb{R}^d,+)$. As an application, that various convolution algebras modules functions satisfy the property.