diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index ed1d346889566..ce3388973458f 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -505,6 +505,32 @@ def test_int_factorize_use_na_sentinel_false(
         tm.assert_numpy_array_equal(uniques, expected_uniques, strict_nan=True)
         tm.assert_numpy_array_equal(codes, expected_codes, strict_nan=True)
 
+    @pytest.mark.parametrize(
+        "data, expected_codes, expected_uniques",
+        [
+            (
+                Index(Categorical(["a", "a", "b"])),
+                np.array([0, 0, 1], dtype=np.intp),
+                CategoricalIndex(["a", "b"], categories=["a", "b"], dtype="category"),
+            ),
+            (
+                Series(Categorical(["a", "a", "b"])),
+                np.array([0, 0, 1], dtype=np.intp),
+                CategoricalIndex(["a", "b"], categories=["a", "b"], dtype="category"),
+            ),
+            (
+                Series(DatetimeIndex(["2017", "2017"], tz="US/Eastern")),
+                np.array([0, 0], dtype=np.intp),
+                DatetimeIndex(["2017"], tz="US/Eastern"),
+            ),
+        ],
+    )
+    def test_factorize_mixed_values(self, data, expected_codes, expected_uniques):
+        # GH 19721
+        codes, uniques = algos.factorize(data)
+        tm.assert_numpy_array_equal(codes, expected_codes)
+        tm.assert_index_equal(uniques, expected_uniques)
+
 
 class TestUnique:
     def test_ints(self):