pratik1709 wrote:
Hi,
Dont need to go with formula.
We konw.. 32 zerores means.. 32 5's and 32 2's.. In any factorial of number, 2s is always be higher than 5's.
Now here Question is howmany odd numbers are possible...
means for any number of zeroes.. there will always 2 odd number..
starting for 1 to 5...1 and 3 are odd number.. whenever it hits 5 , we are adding one more zero to it.
Hope this logic helps.
Hi
pratik1709,
I think above logic might not work always.
if the question had asked number of possible values of odd number n such that 33 trailing zeroes.
then there are three such possible odd numbers, 135!, 137!, 139!
it depends on which parity of n adds that extra zero(es).
say odd number n adds extra zero(es), then there are 3 possible odd number, eg n - 135(odd) adds extra zero to previous 134!, then 135!, 137! and 139! are possible odd numbers of n such that n! has 33 trailing zeroes
say even number n adds extra zero(es), then there are 2 possible odd number.e.g n = 130(even) adds extra zero to previous 129!, then 131! and 133! are only possible numbers of n such that n! has 32 trailing zeroes