I get the following results on my machine:

``````Python 3.2.2 (default, Sep  4 2011, 09:51:08) [MSC v.1500 32 bit (Intel)] on win
32
>>> import timeit
>>> timeit.timeit('factorial(10000)', 'from math import factorial', number=100)
1.9785256226699202
>>>

Python 2.7.2 (default, Jun 12 2011, 15:08:59) [MSC v.1500 32 bit (Intel)] on win
32
>>> import timeit
>>> timeit.timeit('factorial(10000)', 'from math import factorial', number=100)
9.403801111593792
>>>
``````

I thought this might have something to do with int/long conversion, but `factorial(10000L)` isn’t any faster in 2.7.

Python 2 uses the naive factorial algorithm:

``````1121 for (i=1 ; i<=x ; i++) {
1122     iobj = (PyObject *)PyInt_FromLong(i);
1123     if (iobj == NULL)
1124         goto error;
1125     newresult = PyNumber_Multiply(result, iobj);
1126     Py_DECREF(iobj);
1127     if (newresult == NULL)
1128         goto error;
1129     Py_DECREF(result);
1130     result = newresult;
1131 }
``````

Python 3 uses the divide-and-conquer factorial algorithm:

```1229 * factorial(n) is written in the form 2**k * m, with m odd. k and m are
1230 * computed separately, and then combined using a left shift.
```

See the Python Bugtracker issue for the discussion. Thanks DSM for pointing that out.