We need to calculate the number of zeros at the end of X = 50!satyavegi wrote:Q. X is the product of each integer from 1 to 50 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
To get one zero at the end of a number we a pair of 2 and 5 in its factors. As number of 5s are less than number of 2s, let us calculate number of 5s in X.
The sources of 5s in X are 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of 5, 10, 15, 20, 30, 35, 40, and 45 will contribute one 5 and 25 and 50 will contribute one 5s each.
Hence, total number of 5s as factor in X = (1*8 + 2*2) = 12
Hence, there will be 12 zeros at the end of X.
Hence, number of times X can be completely divided by 100 is (12/2) = 6
Therefore, k = 6
The correct answer is C.
