diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2026-11-02-05-50-35.gh-issue-160872.x8NvzN.rst b/Misc/NEWS.d/next/Core_and_Builtins/2026-11-02-05-50-35.gh-issue-160872.x8NvzN.rst
new file mode 100644
index 000000000000000..2911abe2f166f1c
--- /dev/null
+++ b/Misc/NEWS.d/next/Core_and_Builtins/2026-11-02-05-50-35.gh-issue-160872.x8NvzN.rst
@@ -0,0 +1 @@
+Optimize division and remainder operations on large :class:`int` values.
diff --git a/Objects/longobject.c b/Objects/longobject.c
index f5526213944011c..e01eca6b865d6e2 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -3325,8 +3325,7 @@ x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem)
     int d;
     digit wm1, wm2, carry, q, r, vtop, *v0, *vk, *w0, *ak;
     twodigits vv;
-    sdigit zhi;
-    stwodigits z;
+    stwodigits z, zhi;
 
     /* We follow Knuth [The Art of Computer Programming, Vol. 2 (3rd
        edn.), section 4.3.1, Algorithm D], except that we don't explicitly
@@ -3416,16 +3415,15 @@ x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem)
         for (i = 0; i < size_w; ++i) {
             /* invariants: -PyLong_BASE <= -q <= zhi <= 0;
                -PyLong_BASE * q <= z < PyLong_BASE */
-            z = (sdigit)vk[i] + zhi -
+            z = (stwodigits)vk[i] + zhi -
                 (stwodigits)q * (stwodigits)w0[i];
             vk[i] = (digit)z & PyLong_MASK;
-            zhi = (sdigit)Py_ARITHMETIC_RIGHT_SHIFT(stwodigits,
-                                                    z, PyLong_SHIFT);
+            zhi = Py_ARITHMETIC_RIGHT_SHIFT(stwodigits, z, PyLong_SHIFT);
         }
 
         /* add w back if q was too large (this branch taken rarely) */
-        assert((sdigit)vtop + zhi == -1 || (sdigit)vtop + zhi == 0);
-        if ((sdigit)vtop + zhi < 0) {
+        assert((stwodigits)vtop + zhi == -1 || (stwodigits)vtop + zhi == 0);
+        if ((stwodigits)vtop + zhi < 0) {
             carry = 0;
             for (i = 0; i < size_w; ++i) {
                 carry += vk[i] + w0[i];