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 ?

  • 1
    $\begingroup$ If the number is initially close to a power of five, it remains so ! $\endgroup$
    – user65203
    Feb 25 '19 at 13:21

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