We study the computational complexity of the membership problem for arithmetic circuits over natural numbers with division. We consider different subsets of the operations \(\{\cup , \cap , ^{{-}}, +, \times , / \}\) , where / is the element-wise integer division (without remainder and without rounding). Results for the subsets without division have been studied before, in particular by McKenzie and Wagner [12] and Yang [20]. The division is expressive because it makes it possible to describe the set of factors of a given number as a circuit. Surprisingly, the cases \(\{ \cup ,\cap ,^{{-}},+, / \}\) and \(\{ \cup ,\cap ,^{{-}},\times , / \}\) are \(\textrm{PSPACE}\) -complete and therefore equivalent to the corresponding cases without division. The case \(\{ \cup , / \}\) is \(\textrm{NP}\) -hard in contrast to the case \(\{ \cup \}\) which is \(\textrm{NL}\) -complete. Further upper bounds, lower bounds and completeness results are given.