diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 4c9817f3c3dc6..afd6bbb6c57e0 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -51,6 +51,7 @@
     ABCExtensionArray,
     ABCIndexClass,
     ABCMultiIndex,
+    ABCRangeIndex,
     ABCSeries,
 )
 from pandas.core.dtypes.missing import isna, na_value_for_dtype
@@ -682,7 +683,9 @@ def factorize(
         na_sentinel = -1
         dropna = False
 
-    if is_extension_array_dtype(values.dtype):
+    if isinstance(values, ABCRangeIndex):
+        return values.factorize(sort=sort)
+    elif is_extension_array_dtype(values.dtype):
         values = extract_array(values)
         codes, uniques = values.factorize(na_sentinel=na_sentinel)
         dtype = original.dtype
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 8e12f84895361..3222f44dd4415 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -1,7 +1,7 @@
 from datetime import timedelta
 import operator
 from sys import getsizeof
-from typing import Any, List
+from typing import Any, List, Optional, Tuple
 import warnings
 
 import numpy as np
@@ -461,6 +461,16 @@ def argsort(self, *args, **kwargs) -> np.ndarray:
         else:
             return np.arange(len(self) - 1, -1, -1)
 
+    def factorize(
+        self, sort: bool = False, na_sentinel: Optional[int] = -1
+    ) -> Tuple[np.ndarray, "RangeIndex"]:
+        codes = np.arange(len(self), dtype=np.intp)
+        uniques = self
+        if sort and self.step < 0:
+            codes = codes[::-1]
+            uniques = uniques[::-1]
+        return codes, uniques
+
     def equals(self, other: object) -> bool:
         """
         Determines if two Index objects contain the same elements.
diff --git a/pandas/tests/arrays/categorical/test_constructors.py b/pandas/tests/arrays/categorical/test_constructors.py
index dab7fc51f2537..753c15bde6bba 100644
--- a/pandas/tests/arrays/categorical/test_constructors.py
+++ b/pandas/tests/arrays/categorical/test_constructors.py
@@ -290,6 +290,16 @@ def test_constructor_with_generator(self):
         cat = Categorical([0, 1, 2], categories=range(3))
         tm.assert_categorical_equal(cat, exp)
 
+    def test_constructor_with_rangeindex(self):
+        # RangeIndex is preserved in Categories
+        rng = Index(range(3))
+
+        cat = Categorical(rng)
+        tm.assert_index_equal(cat.categories, rng, exact=True)
+
+        cat = Categorical([1, 2, 0], categories=rng)
+        tm.assert_index_equal(cat.categories, rng, exact=True)
+
     @pytest.mark.parametrize(
         "dtl",
         [
diff --git a/pandas/tests/indexes/multi/test_constructors.py b/pandas/tests/indexes/multi/test_constructors.py
index 85f3d17fdd0d4..ca6387938d747 100644
--- a/pandas/tests/indexes/multi/test_constructors.py
+++ b/pandas/tests/indexes/multi/test_constructors.py
@@ -477,6 +477,14 @@ def test_from_product_datetimeindex():
     tm.assert_numpy_array_equal(mi.values, etalon)
 
 
+def test_from_product_rangeindex():
+    # RangeIndex is preserved by factorize, so preserved in levels
+    rng = Index(range(5))
+    other = ["a", "b"]
+    mi = MultiIndex.from_product([rng, other])
+    tm.assert_index_equal(mi._levels[0], rng, exact=True)
+
+
 @pytest.mark.parametrize("ordered", [False, True])
 @pytest.mark.parametrize("f", [lambda x: x, lambda x: Series(x), lambda x: x.values])
 def test_from_product_index_series_categorical(ordered, f):
diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index 89d0a6723c890..d836ca7a53249 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -307,6 +307,39 @@ def test_datetime64_factorize(self, writable):
         tm.assert_numpy_array_equal(codes, expected_codes)
         tm.assert_numpy_array_equal(uniques, expected_uniques)
 
+    @pytest.mark.parametrize("sort", [True, False])
+    def test_factorize_rangeindex(self, sort):
+        # increasing -> sort doesn't matter
+        ri = pd.RangeIndex.from_range(range(10))
+        expected = np.arange(10, dtype=np.intp), ri
+
+        result = algos.factorize(ri, sort=sort)
+        tm.assert_numpy_array_equal(result[0], expected[0])
+        tm.assert_index_equal(result[1], expected[1], exact=True)
+
+        result = ri.factorize(sort=sort)
+        tm.assert_numpy_array_equal(result[0], expected[0])
+        tm.assert_index_equal(result[1], expected[1], exact=True)
+
+    @pytest.mark.parametrize("sort", [True, False])
+    def test_factorize_rangeindex_decreasing(self, sort):
+        # decreasing -> sort matters
+        ri = pd.RangeIndex.from_range(range(10))
+        expected = np.arange(10, dtype=np.intp), ri
+
+        ri2 = ri[::-1]
+        expected = expected[0], ri2
+        if sort:
+            expected = expected[0][::-1], expected[1][::-1]
+
+        result = algos.factorize(ri2, sort=sort)
+        tm.assert_numpy_array_equal(result[0], expected[0])
+        tm.assert_index_equal(result[1], expected[1], exact=True)
+
+        result = ri2.factorize(sort=sort)
+        tm.assert_numpy_array_equal(result[0], expected[0])
+        tm.assert_index_equal(result[1], expected[1], exact=True)
+
     def test_deprecate_order(self):
         # gh 19727 - check warning is raised for deprecated keyword, order.
         # Test not valid once order keyword is removed.