Pandas version checks
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[x] I have checked that this issue has not already been reported.
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[x] I have confirmed this bug exists on the latest version of pandas.
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[ ] I have confirmed this bug exists on the main branch of pandas.
Reproducible Example
import pandas as pd
x = pd.Series([1, None], dtype='Int32').to_frame(name='col')
# This is 'Int32Dtype()' as expected
print(pd.MultiIndex.from_frame(x).to_frame()['col'].dtype)
# This is float64
pd.MultiIndex.from_frame(x).factorize()[1].to_frame().iloc[:, 0].dtype
Issue Description
If you factorize an index, it should always be the case that the factorized index has the same dtypes as the original index, but this example shows that sometimes an extension dtype will be dropped and replaced with a more generic one.
(A related bug is that factorize of an Index should preserve column names.)
pd.factorize of a DataFrame with Int32 columns shows similar behaviour.
Expected Behavior
'Int32Dtype()' in both cases
Installed Versions
INSTALLED VERSIONS
------------------
commit : 4665c10899bc413b639194f6fb8665a5c70f7db5
python : 3.9.7
python-bits : 64
OS : Darwin
OS-release : 24.6.0
Version : Darwin Kernel Version 24.6.0: Mon Jul 14 11:30:29 PDT 2025; root:xnu-11417.140.69~1/RELEASE_ARM64_T6000
machine : x86_64
processor : i386
byteorder : little
LC_ALL : None
LANG : en_GB.UTF-8
LOCALE : en_GB.UTF-8
pandas : 2.3.2
numpy : 2.0.2
pytz : 2024.2
dateutil : 2.8.2
pip : 24.3.1
Cython : 0.29.24
sphinx : 4.2.0
IPython : 7.29.0
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.3
blosc : None
bottleneck : 1.4.2
dataframe-api-compat : None
fastparquet : None
fsspec : 2024.6.1
html5lib : 1.1
hypothesis : None
gcsfs : None
jinja2 : 3.1.6
lxml.etree : 5.3.0
matplotlib : 3.9.4
numba : None
numexpr : 2.10.2
odfpy : None
openpyxl : None
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 19.0.0
pyreadstat : None
pytest : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.13.1
sqlalchemy : 2.0.41
tables : N/A
tabulate : 0.9.0
xarray : None
xlrd : 2.0.1
xlsxwriter : None
zstandard : None
tzdata : 2024.2
qtpy : None
pyqt5 : None
Replace this line with the output of pd.show_versions()