diff --git a/doc/source/whatsnew/v0.18.0.txt b/doc/source/whatsnew/v0.18.0.txt
index b2eb7d9d97d58..160a2936cca70 100644
--- a/doc/source/whatsnew/v0.18.0.txt
+++ b/doc/source/whatsnew/v0.18.0.txt
@@ -110,7 +110,7 @@ Range Index
 
 A ``RangeIndex`` has been added to the ``Int64Index`` sub-classes to support a memory saving alternative for common use cases. This has a similar implementation to the python ``range`` object (``xrange`` in python 2), in that it only stores the start, stop, and step values for the index. It will transparently interact with the user API, converting to ``Int64Index`` if needed.
 
-This will now be the default constructed index for ``NDFrame`` objects, rather than previous an ``Int64Index``. (:issue:`939`)
+This will now be the default constructed index for ``NDFrame`` objects, rather than previous an ``Int64Index``. (:issue:`939`, :issue:`12070`)
 
 Previous Behavior:
 
diff --git a/pandas/core/index.py b/pandas/core/index.py
index 63b748ada6afa..8459cbe3f810e 100644
--- a/pandas/core/index.py
+++ b/pandas/core/index.py
@@ -4360,6 +4360,22 @@ def __getitem__(self, key):
         # fall back to Int64Index
         return super_getitem(key)
 
+    def __floordiv__(self, other):
+        if com.is_integer(other):
+            if (len(self) == 0 or
+                    self._start % other == 0 and
+                    self._step % other == 0):
+                start = self._start // other
+                step = self._step // other
+                stop = start + len(self) * step
+                return RangeIndex(start, stop, step, name=self.name,
+                                  fastpath=True)
+            if len(self) == 1:
+                start = self._start // other
+                return RangeIndex(start, start + 1, 1, name=self.name,
+                                  fastpath=True)
+        return self._int64index // other
+
     @classmethod
     def _add_numeric_methods_binary(cls):
         """ add in numeric methods, specialized to RangeIndex """
diff --git a/pandas/tests/test_index.py b/pandas/tests/test_index.py
index 2c909d653df85..b0210c9fde2e9 100644
--- a/pandas/tests/test_index.py
+++ b/pandas/tests/test_index.py
@@ -3733,7 +3733,7 @@ def test_numeric_compat2(self):
         self.assertTrue(result.equals(expected))
 
         result = idx // 1
-        expected = idx._int64index // 1
+        expected = idx
         tm.assert_index_equal(result, expected, exact=True)
 
         # __mul__
@@ -3748,15 +3748,18 @@ def test_numeric_compat2(self):
         tm.assert_index_equal(Index(result.values), expected, exact=True)
 
         # __floordiv__
-        idx = RangeIndex(0, 1000, 2)
-        result = idx // 2
-        expected = idx._int64index // 2
-        tm.assert_index_equal(result, expected, exact=True)
-
-        idx = RangeIndex(0, 1000, 1)
-        result = idx // 2
-        expected = idx._int64index // 2
-        tm.assert_index_equal(result, expected, exact=True)
+        cases_exact = [(RangeIndex(0, 1000, 2), 2, RangeIndex(0, 500, 1)),
+                       (RangeIndex(-99, -201, -3), -3, RangeIndex(33, 67, 1)),
+                       (RangeIndex(0, 1000, 1), 2,
+                        RangeIndex(0, 1000, 1)._int64index // 2),
+                       (RangeIndex(0, 100, 1), 2.0,
+                        RangeIndex(0, 100, 1)._int64index // 2.0),
+                       (RangeIndex(), 50, RangeIndex()),
+                       (RangeIndex(2, 4, 2), 3, RangeIndex(0, 1, 1)),
+                       (RangeIndex(-5, -10, -6), 4, RangeIndex(-2, -1, 1)),
+                       (RangeIndex(-100, -200, 3), 2, RangeIndex())]
+        for idx, div, expected in cases_exact:
+            tm.assert_index_equal(idx // div, expected, exact=True)
 
     def test_constructor_corner(self):
         arr = np.array([1, 2, 3, 4], dtype=object)
@@ -3857,7 +3860,6 @@ def test_is_monotonic(self):
         self.assertTrue(index.is_monotonic_decreasing)
 
     def test_equals(self):
-
         equiv_pairs = [(RangeIndex(0, 9, 2), RangeIndex(0, 10, 2)),
                        (RangeIndex(0), RangeIndex(1, -1, 3)),
                        (RangeIndex(1, 2, 3), RangeIndex(1, 3, 4)),