diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 0749367045dfa9..6618da0176aaad 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -144,8 +144,8 @@ Number-theoretic functions
 
 .. function:: factorial(n)
 
-   Return *n* factorial as an integer.  Raises :exc:`ValueError` if *n* is not integral or
-   is negative.
+   Return *n* factorial as an integer.  Raises :exc:`TypeError` if *n* is not an integer.
+   Raises :exc:`ValueError` if *n* is negative.
 
    .. versionchanged:: 3.10
       Floats with integral values (like ``5.0``) are no longer accepted.
diff --git a/Modules/clinic/mathmodule.c.h b/Modules/clinic/mathmodule.c.h
index 4c2c8acd8f69d8..e2651e5fed69e9 100644
--- a/Modules/clinic/mathmodule.c.h
+++ b/Modules/clinic/mathmodule.c.h
@@ -110,7 +110,8 @@ PyDoc_STRVAR(math_factorial__doc__,
 "\n"
 "Find n!.\n"
 "\n"
-"Raise a ValueError if x is negative or non-integral.");
+"Raises TypeError if n is not an integer.\n"
+"Raises ValueError if n is negative.");
 
 #define MATH_FACTORIAL_METHODDEF    \
     {"factorial", (PyCFunction)math_factorial, METH_O, math_factorial__doc__},