How many trailing zeroes are there in 100! (100 factorial) ?

See Solution : Zeroes in 100!For every factor of 10, there will be one trailing zero similarly for every factor of 5 there will be one trailing zero (as 5*2 =10, and there are enough number of 2’s). But we have to take care of repetitions.

10, 20,…., 90 = 9 zeros

100 = 2 zeros

5, 15, 25……95 = 10 zeros

and 1 extra 5 in each of 25, 50 and 75 = 3 zeros

so total 9+2+10+3 = 24 zeros.

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gaurav mishra says

(100/25) + (100/5) =24

vignesh says

21

puzzlersworld says

@2987c04409bdefa090e286cd5aa8858c:disqus : nopes its 24, see the solution