diff --git a/gtsam/discrete/DiscreteFactorGraph.cpp b/gtsam/discrete/DiscreteFactorGraph.cpp
index b3029111a..0444f47ae 100644
--- a/gtsam/discrete/DiscreteFactorGraph.cpp
+++ b/gtsam/discrete/DiscreteFactorGraph.cpp
@@ -65,23 +65,11 @@ namespace gtsam {
 
   /* ************************************************************************ */
   DecisionTreeFactor DiscreteFactorGraph::product() const {
-    // PRODUCT: multiply all factors
-    gttic(product);
-    DiscreteFactor::shared_ptr product = *this->begin();
+    DiscreteFactor::shared_ptr result = *this->begin();
     for (auto it = this->begin() + 1; it != this->end(); ++it) {
-      if (*it) product = product->multiply(*it);
+      if (*it) result = result->multiply(*it);
     }
-    gttoc(product);
-
-    DecisionTreeFactor = result->toDecisionTreeFactor();
-
-    // Max over all the potentials by pretending all keys are frontal:
-    auto denominator = product.max(product.size());
-
-    // Normalize the product factor to prevent underflow.
-    product = product / (*denominator);
-
-    return product;
+    return result->toDecisionTreeFactor();
   }
 
   /* ************************************************************************ */
@@ -123,12 +111,34 @@ namespace gtsam {
 //      }
 //  }
 
+  /**
+   * @brief Multiply all the `factors`.
+   *
+   * @param factors The factors to multiply as a DiscreteFactorGraph.
+   * @return DecisionTreeFactor
+   */
+  static DecisionTreeFactor DiscreteProduct(
+      const DiscreteFactorGraph& factors) {
+    // PRODUCT: multiply all factors
+    gttic(product);
+    DecisionTreeFactor product = factors.product();
+    gttoc(product);
+
+    // Max over all the potentials by pretending all keys are frontal:
+    auto denominator = product.max(product.size());
+
+    // Normalize the product factor to prevent underflow.
+    product = product / (*denominator);
+
+    return product;
+  }
+
   /* ************************************************************************ */
   // Alternate eliminate function for MPE
   std::pair<DiscreteConditional::shared_ptr, DiscreteFactor::shared_ptr>  //
   EliminateForMPE(const DiscreteFactorGraph& factors,
                   const Ordering& frontalKeys) {
-    DecisionTreeFactor product = factors.product();
+    DecisionTreeFactor product = DiscreteProduct(factors);
 
     // max out frontals, this is the factor on the separator
     gttic(max);
@@ -206,7 +216,7 @@ namespace gtsam {
   std::pair<DiscreteConditional::shared_ptr, DiscreteFactor::shared_ptr>  //
   EliminateDiscrete(const DiscreteFactorGraph& factors,
                     const Ordering& frontalKeys) {
-    DecisionTreeFactor product = factors.product();
+    DecisionTreeFactor product = DiscreteProduct(factors);
 
     // sum out frontals, this is the factor on the separator
     gttic(sum);