Summary: We consider the full transformation semigroup \(T(X)\) on a finite set \(X\). This is the semigroup of all mappings from \(X\) to \(X\) under composition of mappings as the binary operation. For a finite set \(X\), \(T(X)\) has been known to be a unit regular semigroup and strongly unit regular for \(|X|\leq 3\) [P. M. Higgins, J. M. Howie, N. Ruškuc, Proc. R. Soc. Edinb., Sect. A, Math. 128, No. 6, 1355-1369 (1998; Zbl 0920.20056)]. We show further that \(T(X)\) is an \(R\)-strongly unit regular semigroup for a finite set \(X\). The unit regularity of \(T(X)\) is evident in many properties of \(T(X)\) and so we give a detailed study of this semigroup and illustrate many results for this case. In this paper, we provide some combinatorial results relating to the factorization of elements of \(T(X)\) into product of idempotents and units.