diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 1ad60459e8d377..063205ce213f69 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -66,9 +66,9 @@ Number-theoretic and representation functions
    Return the absolute value of *x*.
 
 
-.. function:: factorial(x)
+.. function:: factorial(n)
 
-   Return *x* factorial as an integer.  Raises :exc:`ValueError` if *x* is not integral or
+   Return *n* factorial as an integer.  Raises :exc:`ValueError` if *n* is not integral or
    is negative.
 
    .. deprecated:: 3.9
diff --git a/Modules/clinic/mathmodule.c.h b/Modules/clinic/mathmodule.c.h
index 65f3dd4f520aeb..4ea0bb82b8e2c8 100644
--- a/Modules/clinic/mathmodule.c.h
+++ b/Modules/clinic/mathmodule.c.h
@@ -45,10 +45,10 @@ PyDoc_STRVAR(math_isqrt__doc__,
     {"isqrt", (PyCFunction)math_isqrt, METH_O, math_isqrt__doc__},
 
 PyDoc_STRVAR(math_factorial__doc__,
-"factorial($module, x, /)\n"
+"factorial($module, n, /)\n"
 "--\n"
 "\n"
-"Find x!.\n"
+"Find n!.\n"
 "\n"
 "Raise a ValueError if x is negative or non-integral.");
 
@@ -865,4 +865,4 @@ math_ulp(PyObject *module, PyObject *arg)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=1eae2b3ef19568fa input=a9049054013a1b77]*/
+/*[clinic end generated code: output=6381e7d982ff3711 input=a9049054013a1b77]*/
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 0c7d4de0686213..1be447eed4f8e3 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2091,17 +2091,17 @@ static const unsigned long SmallFactorials[] = {
 /*[clinic input]
 math.factorial
 
-    x as arg: object
+    n as arg: object
     /
 
-Find x!.
+Find n!.
 
 Raise a ValueError if x is negative or non-integral.
 [clinic start generated code]*/
 
 static PyObject *
 math_factorial(PyObject *module, PyObject *arg)
-/*[clinic end generated code: output=6686f26fae00e9ca input=6d1c8105c0d91fb4]*/
+/*[clinic end generated code: output=6686f26fae00e9ca input=713fb771677e8c31]*/
 {
     long x, two_valuation;
     int overflow;