diff --git a/array_api_tests/hypothesis_helpers.py b/array_api_tests/hypothesis_helpers.py
index 7e7294f8..1bab8d34 100644
--- a/array_api_tests/hypothesis_helpers.py
+++ b/array_api_tests/hypothesis_helpers.py
@@ -449,7 +449,7 @@ def two_broadcastable_shapes(draw):
 )
 
 @composite
-def scalars(draw, dtypes, finite=False):
+def scalars(draw, dtypes, finite=False, **kwds):
     """
     Strategy to generate a scalar that matches a dtype strategy
 
@@ -463,12 +463,12 @@ def scalars(draw, dtypes, finite=False):
         return draw(booleans())
     elif dtype == float64:
         if finite:
-            return draw(floats(allow_nan=False, allow_infinity=False))
-        return draw(floats())
+            return draw(floats(allow_nan=False, allow_infinity=False, **kwds))
+        return draw(floats(), **kwds)
     elif dtype == float32:
         if finite:
-            return draw(floats(width=32, allow_nan=False, allow_infinity=False))
-        return draw(floats(width=32))
+            return draw(floats(width=32, allow_nan=False, allow_infinity=False, **kwds))
+        return draw(floats(width=32, **kwds))
     elif dtype == complex64:
         if finite:
             return draw(complex_numbers(width=32, allow_nan=False, allow_infinity=False))
@@ -591,8 +591,16 @@ def two_mutual_arrays(
 def array_and_py_scalar(draw, dtypes):
     """Draw a pair: (array, scalar) or (scalar, array)."""
     dtype = draw(sampled_from(dtypes))
-    scalar_var = draw(scalars(just(dtype), finite=True))
-    array_var = draw(arrays(dtype, shape=shapes(min_dims=1)))
+
+    scalar_var = draw(scalars(just(dtype), finite=True,
+        **{'min_value': 1/ (2<<5), 'max_value': 2<<5}
+    ))
+
+    elements={}
+    if dtype in dh.real_float_dtypes:
+        elements = {'allow_nan': False, 'allow_infinity': False,
+                    'min_value': 1.0 / (2<<5), 'max_value': 2<<5}
+    array_var = draw(arrays(dtype, shape=shapes(min_dims=1), elements=elements))
 
     if draw(booleans()):
         return scalar_var, array_var
diff --git a/array_api_tests/test_operators_and_elementwise_functions.py b/array_api_tests/test_operators_and_elementwise_functions.py
index 129f5c21..d79fd17b 100644
--- a/array_api_tests/test_operators_and_elementwise_functions.py
+++ b/array_api_tests/test_operators_and_elementwise_functions.py
@@ -1816,19 +1816,11 @@ def _filter_zero(x):
         (xp.less_equal, "les_equal", operator.le, {}, xp.bool),
         (xp.greater, "greater", operator.gt, {}, xp.bool),
         (xp.greater_equal, "greater_equal", operator.ge, {}, xp.bool),
-        (xp.remainder, "remainder", operator.mod, {}, None),
-        (xp.floor_divide, "floor_divide", operator.floordiv, {}, None),
     ],
     ids=lambda func_data: func_data[1]  # use names for test IDs
 )
 @given(x1x2=hh.array_and_py_scalar(dh.real_float_dtypes))
 def test_binary_with_scalars_real(func_data, x1x2):
-
-    if func_data[1] == "remainder":
-        assume(_filter_zero(x1x2[1]))
-    if func_data[1] == "floor_divide":
-        assume(_filter_zero(x1x2[0]) and _filter_zero(x1x2[1]))
-
     _check_binary_with_scalars(func_data, x1x2)
 
 
@@ -1847,6 +1839,24 @@ def test_binary_with_scalars_bool(func_data, x1x2):
     _check_binary_with_scalars(func_data, x1x2)
 
 
+@pytest.mark.min_version("2024.12")
+@pytest.mark.parametrize('func_data',
+    # xp_func, name, refimpl, kwargs, expected_dtype
+    [
+
+        (xp.floor_divide, "floor_divide", operator.floordiv, {}, None),
+        (xp.remainder, "remainder", operator.mod, {}, None),
+    ],
+    ids=lambda func_data: func_data[1]  # use names for test IDs
+)
+@given(x1x2=hh.array_and_py_scalar([xp.int64]))
+def test_binary_with_scalars_int(func_data, x1x2):
+
+    assume(_filter_zero(x1x2[1]))
+    assume(_filter_zero(x1x2[0]) and _filter_zero(x1x2[1]))
+    _check_binary_with_scalars(func_data, x1x2)
+
+
 @pytest.mark.min_version("2024.12")
 @pytest.mark.parametrize('func_data',
     # xp_func, name, refimpl, kwargs, expected_dtype