Why on earth do you want the factorial of 4 to 5 digits? I hope you understand that 170! is a monstrous number?
Anyways, coming to the technical part;
This is 170!
7.2574156153079989673967282111292631147169916812964513765... × 10^306 while 171! is this number 1.2410180702176678234248405241031039926166055775016931853... × 10^309
if you notice the first one contains 306 digits in the exponent and the latter contains 309. Your machine an handle 308 digits in the exponent and hence you can't go beyond that value.
Read more about Computer Number Format here
Anyways, coming to the technical part;
This is 170!
7.2574156153079989673967282111292631147169916812964513765... × 10^306 while 171! is this number 1.2410180702176678234248405241031039926166055775016931853... × 10^309
if you notice the first one contains 306 digits in the exponent and the latter contains 309. Your machine an handle 308 digits in the exponent and hence you can't go beyond that value.
Read more about Computer Number Format here
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