An approximate divisor order is a partial order on the positive integers \({\mathbb {N}^+}\) that refines the divisor order and is refined by the additive total order. A previous paper studied such a partial order on \({\mathbb {N}^+}\) , produced using the floor function. A positive integer d is a floor quotient of n, denoted \(d {\preccurlyeq _{1}}n\) , if there is a positive integer k such that \(d = \left\lfloor {{n} / {k}}\right\rfloor \) . The floor quotient relation defines a partial order on the positive integers. This paper studies a family of partial orders, the a-floor quotient relations \({\preccurlyeq _{a}}\) , for \(a \in {\mathbb {N}^+}\) , which interpolate between the floor quotient order and the divisor order on \({\mathbb {N}^+}\) . The paper studies the internal structure of these orders.