Original

The Easiest way is to find the powers of 3 and 7. For ex $\left\lfloor \frac { 25 }{ 3 } \right\rfloor =8\quad +\quad \left\lfloor \frac { 8 }{ 3 } \right\rfloor =2\quad +\quad \left\lfloor \frac { 2 }{ 3 } \right\rfloor =0$ Hence Maximum power of 3 which divides 25! is 8+2=10 Similarly we can find the highest power of 7 It would come out to be 3 Hence as 21= 7*3 Maximum power of 21 which divides 25! is $3$ .