diff --git a/gtsam/discrete/DecisionTreeFactor.h b/gtsam/discrete/DecisionTreeFactor.h
index 804b956fe..a5b82f277 100644
--- a/gtsam/discrete/DecisionTreeFactor.h
+++ b/gtsam/discrete/DecisionTreeFactor.h
@@ -154,17 +154,17 @@ namespace gtsam {
 
     static double safe_div(const double& a, const double& b);
 
-    /// divide by factor f (safely)
+    /**
+     * @brief Divide by factor f (safely).
+     * Division of a factor \f$f(x, y)\f$ by another factor \f$g(y, z)\f$
+     * results in a function which involves all keys
+     * \f$(\frac{f}{g})(x, y, z) = f(x, y) / g(y, z)\f$
+     * 
+     * @param f The DecisinTreeFactor to divide by.
+     * @return DecisionTreeFactor 
+     */
     DecisionTreeFactor operator/(const DecisionTreeFactor& f) const {
-      KeyVector diff;
-      std::set_difference(this->keys().begin(), this->keys().end(),
-                          f.keys().begin(), f.keys().end(),
-                          std::back_inserter(diff));
-      DiscreteKeys keys;
-      for (Key key : diff) {
-        keys.push_back({key, this->cardinality(key)});
-      }
-      return DecisionTreeFactor(keys, apply(f, safe_div));
+      return apply(f, safe_div);
     }
 
     /// Convert into a decision tree
@@ -181,12 +181,12 @@ namespace gtsam {
     }
 
     /// Create new factor by maximizing over all values with the same separator.
-    shared_ptr max(size_t nrFrontals) const {
+    DiscreteFactor::shared_ptr max(size_t nrFrontals) const {
       return combine(nrFrontals, Ring::max);
     }
 
     /// Create new factor by maximizing over all values with the same separator.
-    shared_ptr max(const Ordering& keys) const {
+    DiscreteFactor::shared_ptr max(const Ordering& keys) const {
       return combine(keys, Ring::max);
     }
 
diff --git a/gtsam/discrete/tests/testDecisionTreeFactor.cpp b/gtsam/discrete/tests/testDecisionTreeFactor.cpp
index 7210622d8..ba8714783 100644
--- a/gtsam/discrete/tests/testDecisionTreeFactor.cpp
+++ b/gtsam/discrete/tests/testDecisionTreeFactor.cpp
@@ -116,8 +116,20 @@ TEST(DecisionTreeFactor, Divide) {
   DiscreteKey A(0, 2), S(1, 2);
   DecisionTreeFactor pA = create(A % "99/1"), pS = create(S % "50/50");
   DecisionTreeFactor joint = pA * pS;
+
   DecisionTreeFactor s = joint / pA;
-  EXPECT(assert_equal(pS, s));
+
+  // Factors are not equal due to difference in keys
+  EXPECT(assert_inequal(pS, s));
+
+  // The underlying data should be the same
+  using ADT = AlgebraicDecisionTree<Key>;
+  EXPECT(assert_equal(ADT(pS), ADT(s)));
+
+  KeySet keys(joint.keys());
+  keys.insert(pA.keys().begin(), pA.keys().end());
+  EXPECT(assert_inequal(KeySet(pS.keys()), keys));
+  
 }
 
 /* ************************************************************************* */