# Number of trailing zeroes , alternate approach.

We have the general method to find the number of trailing zeroes in the factorial of a given number , i.e. by dividing it successively by powers of $$5$$ and taking the greatest integer function. Suppose we have a big number , where this method takes a while , since we have to do multiple division steps and then addition , a friend of mine claims that he has a shortcut method for this problem. He has given me the number $$247383000!$$ . I have tried a lot to discover the alternative approach but so far , no success , although I have noticed something peculiar about the above number
At each division steps , the results are close to powers of $$5$$
$$49476600,9895320,1979064,395812,79162,15832,3166,633,126,25,5,1$$ So is this just a coincidence or is there a special case for which we have an alternate approach ?

• If the number is initially close to a power of five, it remains so !
– user65203
Feb 25, 2019 at 13:21