a is the product of each integer from 1 to 50, inclusive and b=100^k, where k is an integer . What is the greatest value of k for which y is a factor of a? Choose the correct option
A) 6 B) 7 C) 8 D) 9 E) 10

Rationale: the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 50 = 50 ! no . of trailing zeros in 50 ! = 50 / 5 + 50 / 5 ^ 2 = 10 + 2 = 12 100 ^ k = 10 ^ 2 k → k = 12 / 2 = 6 a
Answer: A