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Tushar Methi
CAT Preparation Community 9y ago
pl find the number of zeros in following 25*30*35*35*40...........*1500
2
Akhilesh Singh 9y ago
Hi Tushar,
25*30*35*40......*1500 can be written as 5^296(5*6*7*8*9*.....300). So, we have to find the number of zeroes in this expression.
For number of zeroes, we have to look for the highest power of 2 (Because 0 is formed by 5*2 and we have 5 in abundance here)
Number of 2's in 300! = 150 + 75 + 37 + 18 + 9 + 4 + 2 + 1 = 296. But the given number is not exacty is 300!, So, we have to subtract the number of 2's in 4! = 2+1 = 3.
Hence the highest power of 3 in the given number is 296 - 3 = 293.
Thus, the number of trailing zeroes in the given expression will be 293.
aaron k 9y ago
25*30*35*....1500
take 5 as from common form every term
as the no of terms are 296 we will get 5^296 *(5*6*......*300)
now find both no of 2's and no of 5's of the term in the parentheses
so no of twos will be 290 and no of 5s will be 74 so as a whole no of 5's are 370
so no of zeroes will be 290.
