Overflow starts at 13 although it is not immediately obvious.
Factorial grows so fast that the sign bit becomes completely unreliable.

        INT_MAX =  2147483647

Factorial of  1 =           1
Factorial of  2 =           2
Factorial of  3 =           6
Factorial of  4 =          24
Factorial of  5 =         120
Factorial of  6 =         720
Factorial of  7 =        5040
Factorial of  8 =       40320
Factorial of  9 =      362880
Factorial of 10 =     3628800
Factorial of 11 =    39916800
Factorial of 12 =   479001600
Factorial of 13 =  1932053504
Factorial of 14 =  1278945280
Factorial of 15 =  2004310016
Factorial of 16 =  2004189184
Factorial of 17 =  -288522240
Factorial of 18 =  -898433024
Factorial of 19 =   109641728
Factorial of 20 = -2102132736
Factorial of 21 = -1195114496
Factorial of 22 =  -522715136
Factorial of 23 =   862453760
Factorial of 24 =  -775946240