We need max value of n such that the number is divisible by $35^n$.

$35 = 5 \times 7$

So we must find how many times 5 occurs and how many times 7 occurs in the product.

Step 1: Prime factor break down

• 7 → gives $7^1$
• 343 = $7^3$
• 385 = $5 \times 7 \times 11$ → gives one 5 and one 7
• 1000 = $10^3 = 2^3 \times 5^3$ → gives three 5s
• 2401 = $7^4$
• 77777 factors = $7 \times 41 \times 271$ → gives one 7

Total 7's = 10 Total 5's = 4

Key logic:

To form $35^n$, we need both $7^n$ and $5^n$. So take the minimum of the two counts.

Minimum = 4

Correct Answer: B. 4