Summary: We prove that the ultrapower and the central sequence algebra of the hyperfinite \(\text{II}_1\) factor are prime factors which implies that the central sequence algebra of the tensor product of two factors may not be the tensor product of the central sequence algebras of the factors, respectively. This answers negatively a question of D. McDuff [Proc.Lond.Math.Soc.(3) 21, 443–461 (1970; Zbl 0204.14902)]. Isomorphisms of ultrapowers of factors are also studied.