diff --git a/pandas/tests/indexes/common.py b/pandas/tests/indexes/common.py
index 45e1b615b1ade..857b136b67a0c 100644
--- a/pandas/tests/indexes/common.py
+++ b/pandas/tests/indexes/common.py
@@ -831,3 +831,10 @@ def test_arithmetic_explicit_conversions(self):
         a = np.zeros(5, dtype="float64")
         result = a - fidx
         tm.assert_index_equal(result, expected)
+
+    def test_invalid_dtype(self, invalid_dtype):
+        # GH 29539
+        dtype = invalid_dtype
+        msg = fr"Incorrect `dtype` passed: expected \w+(?: \w+)?, received {dtype}"
+        with pytest.raises(ValueError, match=msg):
+            self._index_cls([1, 2, 3], dtype=dtype)
diff --git a/pandas/tests/indexes/numeric/test_numeric.py b/pandas/tests/indexes/numeric/test_numeric.py
index bfe06d74570da..e63aeba54fccd 100644
--- a/pandas/tests/indexes/numeric/test_numeric.py
+++ b/pandas/tests/indexes/numeric/test_numeric.py
@@ -8,7 +8,6 @@
     Float64Index,
     Index,
     Int64Index,
-    RangeIndex,
     Series,
     UInt64Index,
 )
@@ -20,6 +19,12 @@ class TestFloat64Index(NumericBase):
     _index_cls = Float64Index
     _dtype = np.float64
 
+    @pytest.fixture(
+        params=["int64", "uint64", "category", "datetime64"],
+    )
+    def invalid_dtype(self, request):
+        return request.param
+
     @pytest.fixture
     def simple_index(self) -> Index:
         values = np.arange(5, dtype=self._dtype)
@@ -104,23 +109,6 @@ def test_constructor(self):
         assert result.dtype == dtype
         assert pd.isna(result.values).all()
 
-    @pytest.mark.parametrize(
-        "index, dtype",
-        [
-            (Int64Index, "float64"),
-            (UInt64Index, "categorical"),
-            (Float64Index, "datetime64"),
-            (RangeIndex, "float64"),
-        ],
-    )
-    def test_invalid_dtype(self, index, dtype):
-        # GH 29539
-        with pytest.raises(
-            ValueError,
-            match=rf"Incorrect `dtype` passed: expected \w+(?: \w+)?, received {dtype}",
-        ):
-            index([1, 2, 3], dtype=dtype)
-
     def test_constructor_invalid(self):
         index_cls = self._index_cls
         cls_name = index_cls.__name__
@@ -394,6 +382,12 @@ class TestInt64Index(NumericInt):
     _index_cls = Int64Index
     _dtype = np.int64
 
+    @pytest.fixture(
+        params=["uint64", "float64", "category", "datetime64"],
+    )
+    def invalid_dtype(self, request):
+        return request.param
+
     @pytest.fixture
     def simple_index(self) -> Index:
         return self._index_cls(range(0, 20, 2), dtype=self._dtype)
@@ -492,6 +486,12 @@ class TestUInt64Index(NumericInt):
     _index_cls = UInt64Index
     _dtype = np.uint64
 
+    @pytest.fixture(
+        params=["int64", "float64", "category", "datetime64"],
+    )
+    def invalid_dtype(self, request):
+        return request.param
+
     @pytest.fixture
     def simple_index(self) -> Index:
         # compat with shared Int64/Float64 tests
diff --git a/pandas/tests/indexes/ranges/test_range.py b/pandas/tests/indexes/ranges/test_range.py
index 3a4aa29ea620e..12fce56ffcb21 100644
--- a/pandas/tests/indexes/ranges/test_range.py
+++ b/pandas/tests/indexes/ranges/test_range.py
@@ -23,6 +23,12 @@
 class TestRangeIndex(NumericBase):
     _index_cls = RangeIndex
 
+    @pytest.fixture(
+        params=["uint64", "float64", "category", "datetime64"],
+    )
+    def invalid_dtype(self, request):
+        return request.param
+
     @pytest.fixture
     def simple_index(self) -> Index:
         return self._index_cls(start=0, stop=20, step=2)