Maximum power of 35 dividing a product

To find the maximum power of 35 that divides the product, we must find the prime factorization of the given numbers. Since 35 = 5 × 7, we count the total available powers of 5 and 7. 385 = 5^1 × 7^1 × 11. 1000 = 10³ = 2³ × 5³. Total powers of 5 = 1 + 3 = 4. Since there are clearly many more powers of 7 (343=7³, 2401=7^4, plus multiples of 7 in 385 and 777777), the limiting prime factor is 5. The maximum number of 35s we can form is dictated by the smaller exponent, which is 4. Thus, n = 4.

Answer: (b).