diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 0e567972e7823..c40ed43504d89 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -705,6 +705,7 @@ Conversion
 - Bug in :class:`DataFrame` failing to raise ``TypeError`` when constructing from a ``frozenset`` (:issue:`40163`)
 - Bug in :class:`Index` construction silently ignoring a passed ``dtype`` when the data cannot be cast to that dtype (:issue:`21311`)
 - Bug in :meth:`StringArray.astype` falling back to numpy and raising when converting to ``dtype='categorical'`` (:issue:`40450`)
+- Bug in :func:`factorize` where, when given an array with a numeric numpy dtype lower than int64, uint64 and float64, the unique values did not keep their original dtype (:issue:`41132`)
 - Bug in :class:`DataFrame` construction with a dictionary containing an arraylike with ``ExtensionDtype`` and ``copy=True`` failing to make a copy (:issue:`38939`)
 -
 
diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 6f906cf8879ff..6a17174c6c0a8 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -143,11 +143,11 @@ def _ensure_data(values: ArrayLike) -> tuple[np.ndarray, DtypeObj]:
             # until our algos support uint8 directly (see TODO)
             return np.asarray(values).astype("uint64"), np.dtype("bool")
         elif is_signed_integer_dtype(values):
-            return ensure_int64(values), np.dtype("int64")
+            return ensure_int64(values), values.dtype
         elif is_unsigned_integer_dtype(values):
-            return ensure_uint64(values), np.dtype("uint64")
+            return ensure_uint64(values), values.dtype
         elif is_float_dtype(values):
-            return ensure_float64(values), np.dtype("float64")
+            return ensure_float64(values), values.dtype
         elif is_complex_dtype(values):
 
             # ignore the fact that we are casting to float
diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index 75fc7a782772a..c7af104f62770 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -95,29 +95,32 @@ def test_basic(self):
         exp = np.array(["a", "b", "c"], dtype=object)
         tm.assert_numpy_array_equal(uniques, exp)
 
-        codes, uniques = algos.factorize(list(reversed(range(5))))
+        arr = np.arange(5, dtype=np.intp)[::-1]
+
+        codes, uniques = algos.factorize(arr)
         exp = np.array([0, 1, 2, 3, 4], dtype=np.intp)
         tm.assert_numpy_array_equal(codes, exp)
-        exp = np.array([4, 3, 2, 1, 0], dtype=np.int64)
+        exp = np.array([4, 3, 2, 1, 0], dtype=arr.dtype)
         tm.assert_numpy_array_equal(uniques, exp)
 
-        codes, uniques = algos.factorize(list(reversed(range(5))), sort=True)
-
+        codes, uniques = algos.factorize(arr, sort=True)
         exp = np.array([4, 3, 2, 1, 0], dtype=np.intp)
         tm.assert_numpy_array_equal(codes, exp)
-        exp = np.array([0, 1, 2, 3, 4], dtype=np.int64)
+        exp = np.array([0, 1, 2, 3, 4], dtype=arr.dtype)
         tm.assert_numpy_array_equal(uniques, exp)
 
-        codes, uniques = algos.factorize(list(reversed(np.arange(5.0))))
+        arr = np.arange(5.0)[::-1]
+
+        codes, uniques = algos.factorize(arr)
         exp = np.array([0, 1, 2, 3, 4], dtype=np.intp)
         tm.assert_numpy_array_equal(codes, exp)
-        exp = np.array([4.0, 3.0, 2.0, 1.0, 0.0], dtype=np.float64)
+        exp = np.array([4.0, 3.0, 2.0, 1.0, 0.0], dtype=arr.dtype)
         tm.assert_numpy_array_equal(uniques, exp)
 
-        codes, uniques = algos.factorize(list(reversed(np.arange(5.0))), sort=True)
+        codes, uniques = algos.factorize(arr, sort=True)
         exp = np.array([4, 3, 2, 1, 0], dtype=np.intp)
         tm.assert_numpy_array_equal(codes, exp)
-        exp = np.array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=np.float64)
+        exp = np.array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=arr.dtype)
         tm.assert_numpy_array_equal(uniques, exp)
 
     def test_mixed(self):
@@ -246,6 +249,17 @@ def test_complex_sorting(self):
         with pytest.raises(TypeError, match=msg):
             algos.factorize(x17[::-1], sort=True)
 
+    def test_numeric_dtype_factorize(self, any_real_dtype):
+        # GH41132
+        dtype = any_real_dtype
+        data = np.array([1, 2, 2, 1], dtype=dtype)
+        expected_codes = np.array([0, 1, 1, 0], dtype=np.intp)
+        expected_uniques = np.array([1, 2], dtype=dtype)
+
+        codes, uniques = algos.factorize(data)
+        tm.assert_numpy_array_equal(codes, expected_codes)
+        tm.assert_numpy_array_equal(uniques, expected_uniques)
+
     def test_float64_factorize(self, writable):
         data = np.array([1.0, 1e8, 1.0, 1e-8, 1e8, 1.0], dtype=np.float64)
         data.setflags(write=writable)