If the integer represented by 100 ! has K consective zeroes at the end, then K=

Step-by-step solution

The number of zeroes in the product depends on the number of times, the 10 is multiplied. So, we need to find the number of pairs of 5 and 2 . As the numbers are all in sequence, there will obviously more 2 then 5 . So, the numbers containing factors 5 is 5,10,15,20,25,30,35,40,45,50,55,60,65,70 , 75,80,85,90,95 and 100 . Number of factors containing factor 5=20 However, 25, 50, 75, 100 contain 5 twice. So, total number of factors =20+4=24 Hence, the entire product contain 10 is 24 times. So, in 100 ! number of con