<s>[INST] Find the highest power of prime which divides a factorial. Find the highest power of $10$ that divides $50!$.
I know by De-Polignac's formula ,the highest power of $5$ that divides $50!$ is $12$ & the highest power of $2$ that divides $50!$ is $47$.
I am able to find this because $5$ & $2$ are primes but here $10$ is not prime but $10=5 \times 2$ so what can we say about the power of 10

My observation say that it may be $47-12$
  Please correct me

 [/INST] As you found:
The highest power of $2$ that divides $50!$ is $\left\lfloor \frac{50}{2} \right \rfloor + \left\lfloor \frac{50}{2^2} \right \rfloor + \left\lfloor \frac{50}{2^3} \right \rfloor  + \cdots$ which evaluates as $ 25+12+6+3+1$ $= 47$, each term being half-rounded-down of the previous one.
The highest power of $5$ that divides $50!$ is $\left\lfloor \frac{50}{5} \right \rfloor + \left\lfloor \frac{50}{5^2} \right \rfloor = 10+2= 12$, similarly dividing through by $5$ repeatedly.

So $50! = k\cdot 2^{47}\cdot 5^{12}$, where $k$ is not divisible by either $2$ or $5$. Clearly we can also write this as $50! = k\cdot 2^{35}\cdot 10^{12}$ - and again $k$ is coprime to both $2$ and $10$.
So the result is that $50!$ is divisible by $10^{12}$ but not by  $10^{13}$, since here the powers of $5$ determine how many powers of $10$ can be extracted from $50!$. 
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