diff --git a/pandas/_libs/tslibs/nattype.pyx b/pandas/_libs/tslibs/nattype.pyx
index 3a61de62daf39..d5582d65a0c11 100644
--- a/pandas/_libs/tslibs/nattype.pyx
+++ b/pandas/_libs/tslibs/nattype.pyx
@@ -286,12 +286,6 @@ cdef class _NaT(datetime):
     def __hash__(self):
         return NPY_NAT
 
-    def __int__(self):
-        return NPY_NAT
-
-    def __long__(self):
-        return NPY_NAT
-
     @property
     def is_leap_year(self) -> bool:
         return False
diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index ae7e8191fc482..3927fb04187f5 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -715,7 +715,7 @@ def factorize(
         values, dtype = _ensure_data(values)
 
         if original.dtype.kind in ["m", "M"]:
-            na_value = na_value_for_dtype(original.dtype)
+            na_value = iNaT
         else:
             na_value = None
 
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 435da1ed062e6..1032559766ada 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1607,7 +1607,7 @@ def _round(self, freq, mode, ambiguous, nonexistent):
 
         values = self.view("i8")
         result = round_nsint64(values, mode, freq)
-        result = self._maybe_mask_results(result, fill_value=NaT)
+        result = self._maybe_mask_results(result, fill_value=iNaT)
         return self._simple_new(result, dtype=self.dtype)
 
     @Appender((_round_doc + _round_example).format(op="round"))
diff --git a/pandas/tests/arithmetic/test_timedelta64.py b/pandas/tests/arithmetic/test_timedelta64.py
index 5f3d2040b0201..c4afe971d533e 100644
--- a/pandas/tests/arithmetic/test_timedelta64.py
+++ b/pandas/tests/arithmetic/test_timedelta64.py
@@ -679,7 +679,7 @@ def test_tdi_add_overflow(self):
         with pytest.raises(OutOfBoundsDatetime, match="10155196800000000000"):
             Timestamp("2000") + pd.to_timedelta(106580, "D")
 
-        _NaT = int(pd.NaT) + 1
+        _NaT = pd.NaT.value + 1
         msg = "Overflow in int64 addition"
         with pytest.raises(OverflowError, match=msg):
             pd.to_timedelta([106580], "D") + Timestamp("2000")
diff --git a/pandas/tests/frame/methods/test_sort_values.py b/pandas/tests/frame/methods/test_sort_values.py
index cd3286fa38056..86c9e2f5ffe52 100644
--- a/pandas/tests/frame/methods/test_sort_values.py
+++ b/pandas/tests/frame/methods/test_sort_values.py
@@ -323,7 +323,7 @@ def test_sort_values_nat_values_in_int_column(self):
         # cause was that the int64 value NaT was considered as "na". Which is
         # only correct for datetime64 columns.
 
-        int_values = (2, int(NaT))
+        int_values = (2, int(NaT.value))
         float_values = (2.0, -1.797693e308)
 
         df = DataFrame(