Problem: x is the product of each integer from 1 to 25 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
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 . . . . * 25 = 25 ! no . of trailing zeros in 25 ! = 25 / 5 + 25 / 5 ^ 2 = 6 100 ^ k = 10 ^ 2 k → k = 6 / 2 = 3 c"
annotated_formula: add(divide(25, const_10), 1)