To find number of zeroes at the end of any number factorial

To find number of zeroes at the end of any number factorial,
you have to count number of zeroes i.e. multiplication by 10 and 5 in the series.
e.g. 10! number of 5 and 10 there are 1 + 1 = 2 so number of zeroes = 2
in case of 25! number of 5 are, 5, 15, 25 (contains 2 fives)
and number of zeroes in 10 and 20
so total number of zeroes at the end in the product is 4 + 2 = 6
But in longer series it is difficult to count number of zeroes and fives
to find
divide the last number i.e. 25 by 5 and go on dividing the quotient by5 till the quotient is zero. add all quotients will give number of zeroes at the end of product.
25/5 = 5
5/5 = 1
number of zeroes = 5 + 1 = 6

in 200!
200/5 = 40
40/5 = 8
8/5 = 1
1/5 = 0
number of zeroes = 40 + 8 + 1 = 49

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PUZZELS

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