How many zeros?

[patelv]

If a=1^2, b=2^3, c=3^4, d=4^5...........z=26^27,then how many zeros would be present in the end in the product of all alpahabets?

[Rahul@gurome]

For this we need to calculate the number of 5's in the product which will combine with 2's to give a zero in the end. We need not calculate the number of 2's because they are much more than no. of 5's.

5^6 has 6 fives.
10^11 is 2^11*5^11 which gives 11 fives.
15^16 is 3^16*5^16 which gives 16 fives.
20^21 is 4^21*5^21 which gives 21 fives.
25^26 is 5^52 which has 52 fives.

So total number of zeroes in the end is 6+11+16+21+52 = 106