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

35 = 5 × 7. Powers of 5: 385 gives 1 and 1000 gives 3, total 4. Powers of 7 are far more (10). So n = 4. (Answer as per the official UPSC answer key.)