The statistical distribution function of anyon is used to find the eighth viral coefficient in the high-temperature limit and the equation of state in the low-temperature limit. The perturbative results indicate that the thermodynamic quantities, $Q(α)$, of the free anyon gas may be factorized in the terms characteristic of the ideal Bose ($α=0$) and fermion ($α=1$) gases, i.e., $Q(α) = αQ(1) + (1-α) Q(0)$. It is shown that the factorizable property of the thermodynamic quantities, to all orders, can be established from the property of the equivalence between the anyon statistics and statistics in a system with boson-fermion transmutation, which was found by us in a recent paper (hep-th/0308095; Phys. Rev. E 51 (1995) 3729)