diff --git a/Tests/test_image_reduce.py b/Tests/test_image_reduce.py
index 6771b46b051..1f28f330e77 100644
--- a/Tests/test_image_reduce.py
+++ b/Tests/test_image_reduce.py
@@ -53,6 +53,22 @@ def test_args_factor(size: int | tuple[int, int], expected: tuple[int, int]) ->
     assert expected == im.reduce(size).size
 
 
+@pytest.mark.parametrize("mode", ("L", "I", "F"))
+@pytest.mark.parametrize(
+    "size, expected",
+    (
+        (2**31 - 1, (1, 1)),
+        ((2**31 - 1, 1), (1, 10)),
+        ((1, 2**31 - 1), (10, 1)),
+    ),
+)
+def test_args_factor_large(
+    size: int | tuple[int, int], expected: tuple[int, int], mode: str
+) -> None:
+    im = Image.new(mode, (10, 10))
+    assert im.reduce(size).size == expected
+
+
 @pytest.mark.parametrize(
     "size, expected_error", ((0, ValueError), (2.0, TypeError), ((0, 10), ValueError))
 )
diff --git a/src/libImaging/Reduce.c b/src/libImaging/Reduce.c
index a4e58ced81b..c4cb4bc76be 100644
--- a/src/libImaging/Reduce.c
+++ b/src/libImaging/Reduce.c
@@ -1460,8 +1460,11 @@ ImagingReduce(Imaging imIn, int xscale, int yscale, int box[4]) {
         return (Imaging)ImagingError_ModeError();
     }
 
+    /* Round the size up. Dividing before adding avoids overflowing for a
+       large scale, and guarantees a size of at least 1x1.
+     */
     imOut = ImagingNewDirty(
-        imIn->mode, (box[2] + xscale - 1) / xscale, (box[3] + yscale - 1) / yscale
+        imIn->mode, (box[2] - 1) / xscale + 1, (box[3] - 1) / yscale + 1
     );
     if (!imOut) {
         return NULL;