Inspired by Melissa Quail

Power of x ,where x is a prime ,in n! is $\left\lfloor \frac { n }{ x } \right\rfloor +\left\lfloor \frac { n }{ { x }^{ 2 } } \right\rfloor +\left\lfloor \frac { n }{ { x }^{ 3 } } \right\rfloor +.....+\left\lfloor \frac { n }{ { x }^{ a } } \right\rfloor$ where the summation ends if the last term is zero.

Note, 175 is not a prime number . So you have to split it into primes and find the powers of individual primes . $175={ 5 }^{ 2 }\times 7$ . Power of 5 in 1175! is 292 and of 7 is 193 (we have found the powers by the above formula). But we don't want the power of 5, as for eg if we have three 5's , then there is only one 25.So power of 25 is half the power of 5. We now have power of 25 as 146 and power of 7 as 193 Therefore, for one forty-six 25's we have one forty-six 7's. Using them we can form one forty six 175's .Hence, power of 175 is 146.