diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index 129f5cedb86c2..75971f4ca109e 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -776,6 +776,7 @@ Timezones
 Numeric
 ^^^^^^^
 - Bug in :func:`read_csv` with ``engine="pyarrow"`` causing rounding errors for large integers (:issue:`52505`)
+- Bug in :meth:`Series.__floordiv__` and :meth:`Series.__truediv__` for :class:`ArrowDtype` with integral dtypes raising for large divisors (:issue:`56706`)
 - Bug in :meth:`Series.__floordiv__` for :class:`ArrowDtype` with integral dtypes raising for large values (:issue:`56645`)
 - Bug in :meth:`Series.pow` not filling missing values correctly (:issue:`55512`)
 
diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index b1164301e6d79..c7de54c6ee84b 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -109,7 +109,7 @@
 
     def cast_for_truediv(
         arrow_array: pa.ChunkedArray, pa_object: pa.Array | pa.Scalar
-    ) -> pa.ChunkedArray:
+    ) -> tuple[pa.ChunkedArray, pa.Array | pa.Scalar]:
         # Ensure int / int -> float mirroring Python/Numpy behavior
         # as pc.divide_checked(int, int) -> int
         if pa.types.is_integer(arrow_array.type) and pa.types.is_integer(
@@ -120,8 +120,15 @@ def cast_for_truediv(
             # Intentionally not using arrow_array.cast because it could be a scalar
             # value in reflected case, and safe=False only added to
             # scalar cast in pyarrow 13.
-            return pc.cast(arrow_array, pa.float64(), safe=False)
-        return arrow_array
+            # In arrow, common type between integral and float64 is float64,
+            # but integral type is safe casted to float64, to mirror python
+            # and numpy, we want an unsafe cast, so we cast both operands to
+            # to float64 before invoking arrow.
+            return pc.cast(arrow_array, pa.float64(), safe=False), pc.cast(
+                pa_object, pa.float64(), safe=False
+            )
+
+        return arrow_array, pa_object
 
     def floordiv_compat(
         left: pa.ChunkedArray | pa.Array | pa.Scalar,
@@ -129,8 +136,8 @@ def floordiv_compat(
     ) -> pa.ChunkedArray:
         # Ensure int // int -> int mirroring Python/Numpy behavior
         # as pc.floor(pc.divide_checked(int, int)) -> float
-        converted_left = cast_for_truediv(left, right)
-        result = pc.floor(pc.divide(converted_left, right))
+        converted_left, converted_right = cast_for_truediv(left, right)
+        result = pc.floor(pc.divide(converted_left, converted_right))
         if pa.types.is_integer(left.type) and pa.types.is_integer(right.type):
             result = result.cast(left.type)
         return result
@@ -142,8 +149,8 @@ def floordiv_compat(
         "rsub": lambda x, y: pc.subtract_checked(y, x),
         "mul": pc.multiply_checked,
         "rmul": lambda x, y: pc.multiply_checked(y, x),
-        "truediv": lambda x, y: pc.divide(cast_for_truediv(x, y), y),
-        "rtruediv": lambda x, y: pc.divide(y, cast_for_truediv(x, y)),
+        "truediv": lambda x, y: pc.divide(*cast_for_truediv(x, y)),
+        "rtruediv": lambda x, y: pc.divide(*cast_for_truediv(y, x)),
         "floordiv": lambda x, y: floordiv_compat(x, y),
         "rfloordiv": lambda x, y: floordiv_compat(y, x),
         "mod": NotImplemented,
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index ed1b7b199a16f..24b2ac4fa8b22 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -3246,6 +3246,24 @@ def test_arrow_floordiv_large_values():
     tm.assert_series_equal(result, expected)
 
 
+def test_arrow_true_division_large_divisor():
+    # GH 56706
+    a = pd.Series([0], dtype="int64[pyarrow]")
+    b = pd.Series([18014398509481983], dtype="int64[pyarrow]")
+    expected = pd.Series([0], dtype="float64[pyarrow]")
+    result = a / b
+    tm.assert_series_equal(result, expected)
+
+
+def test_arrow_floor_division_large_divisor():
+    # GH 56706
+    a = pd.Series([0], dtype="int64[pyarrow]")
+    b = pd.Series([18014398509481983], dtype="int64[pyarrow]")
+    expected = pd.Series([0], dtype="int64[pyarrow]")
+    result = a // b
+    tm.assert_series_equal(result, expected)
+
+
 def test_string_to_datetime_parsing_cast():
     # GH 56266
     string_dates = ["2020-01-01 04:30:00", "2020-01-02 00:00:00", "2020-01-03 00:00:00"]