Concept:The highest power of the prime number p in n! = \(\displaystyle \frac{n}{p^1}+\frac{n}{p^2}+\frac{n}{p^3}.....\)Calculation:(30! + 35!)? (30! + 35 × 34 × 33 × 32 × 31 × 30!) ? 30! (1 + 35 × 34 × 33 × 32 × 31)? 30! (1 + 7 × 5 × 17 × 2 × 3 × 11 × 25 × 31)Now, the number of fives in 30! is given by \(\displaystyle \frac{30}{5^1}+\frac{30}{5^2}+\frac{30}{5^3}= 6+1+0=7\)So, 30! has 7 fives, and (1 + 7 × 5 × 17 × 2 × 3 × 11 × 25 × 31) has zero 5. ? The max number of 5s is 7 i.e. n = 7