What is the maximum value of n such that 7 x 343 × 385 × 1000 × 2401 × 77777 is divisible by 35^n?

1. **Analyze the Goal:** We need the maximum power $n$ for $35^n$. Since $35 = 5 \times 7$, every unit of $n$ requires one '5' and one '7' from the product. We need to find how many such pairs we can form. The answer will be dete