Directly, I can calculate at most:

Even with  factorial 1  I can calculate at most 170!.

But with  + × integers  I can calculate the factorial of larger numbers.  An example:  172!

72574156153079989673967282111292631147169916812964513765435777989005618
43401706157852350749242617459511490991237838520776666022565442753025328
90077320751090240043028005829560396661259965825710439855829425756896631
34396122625710949468067112055688804571933402126614528000000000000000000
00000000000000000000000 x 171 =
12410180702176678234248405241031039926166055775016931853889518036119960
75221691752992751978120487585576464959501670387052809889858690710767331
24203221848436431047357788996854827829075454156196485215346831804429323
95981736968996572359039476161522785581800611763651084288000000000000000
00000000000000000000000000

12410180702176678234248405241031039926166055775016931853889518036119960
75221691752992751978120487585576464959501670387052809889858690710767331
24203221848436431047357788996854827829075454156196485215346831804429323
95981736968996572359039476161522785581800611763651084288000000000000000
00000000000000000000000000 x 172 =
21345510807743886562907257014573388673005615933029122788689971022126332
49381309815147533402367238647191519730342873065730833010556948022519809
73629541579310661401455397074590303866009781148657954570396550703618437
21088587586674104457547898997819191200697052233479864975360000000000000
0000000000000000000000000000