diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index e818e367ca83d..b6fa5da857910 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -2364,35 +2364,7 @@ def _factorize_keys(
             # "_values_for_factorize"
             rk, _ = rk._values_for_factorize()  # type: ignore[union-attr]
 
-    klass: type[libhashtable.Factorizer]
-    if is_numeric_dtype(lk.dtype):
-        if not is_dtype_equal(lk, rk):
-            dtype = find_common_type([lk.dtype, rk.dtype])
-            if isinstance(dtype, ExtensionDtype):
-                cls = dtype.construct_array_type()
-                if not isinstance(lk, ExtensionArray):
-                    lk = cls._from_sequence(lk, dtype=dtype, copy=False)
-                else:
-                    lk = lk.astype(dtype)
-
-                if not isinstance(rk, ExtensionArray):
-                    rk = cls._from_sequence(rk, dtype=dtype, copy=False)
-                else:
-                    rk = rk.astype(dtype)
-            else:
-                lk = lk.astype(dtype)
-                rk = rk.astype(dtype)
-        if isinstance(lk, BaseMaskedArray):
-            #  Invalid index type "type" for "Dict[Type[object], Type[Factorizer]]";
-            #  expected type "Type[object]"
-            klass = _factorizers[lk.dtype.type]  # type: ignore[index]
-        else:
-            klass = _factorizers[lk.dtype.type]
-
-    else:
-        klass = libhashtable.ObjectFactorizer
-        lk = ensure_object(lk)
-        rk = ensure_object(rk)
+    klass, lk, rk = _convert_arrays_and_get_rizer_klass(lk, rk)
 
     rizer = klass(max(len(lk), len(rk)))
 
@@ -2433,6 +2405,41 @@ def _factorize_keys(
     return llab, rlab, count
 
 
+def _convert_arrays_and_get_rizer_klass(
+    lk: ArrayLike, rk: ArrayLike
+) -> tuple[type[libhashtable.Factorizer], ArrayLike, ArrayLike]:
+    klass: type[libhashtable.Factorizer]
+    if is_numeric_dtype(lk.dtype):
+        if not is_dtype_equal(lk, rk):
+            dtype = find_common_type([lk.dtype, rk.dtype])
+            if isinstance(dtype, ExtensionDtype):
+                cls = dtype.construct_array_type()
+                if not isinstance(lk, ExtensionArray):
+                    lk = cls._from_sequence(lk, dtype=dtype, copy=False)
+                else:
+                    lk = lk.astype(dtype)
+
+                if not isinstance(rk, ExtensionArray):
+                    rk = cls._from_sequence(rk, dtype=dtype, copy=False)
+                else:
+                    rk = rk.astype(dtype)
+            else:
+                lk = lk.astype(dtype)
+                rk = rk.astype(dtype)
+        if isinstance(lk, BaseMaskedArray):
+            #  Invalid index type "type" for "Dict[Type[object], Type[Factorizer]]";
+            #  expected type "Type[object]"
+            klass = _factorizers[lk.dtype.type]  # type: ignore[index]
+        else:
+            klass = _factorizers[lk.dtype.type]
+
+    else:
+        klass = libhashtable.ObjectFactorizer
+        lk = ensure_object(lk)
+        rk = ensure_object(rk)
+    return klass, lk, rk
+
+
 def _sort_labels(
     uniques: np.ndarray, left: npt.NDArray[np.intp], right: npt.NDArray[np.intp]
 ) -> tuple[npt.NDArray[np.intp], npt.NDArray[np.intp]]: