A number theory problem by Murad Al Wajed
Find the number of trailing number of zeros in the number .
(In mathematics, trailing zeros are a sequence of 0's in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow.)
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1 solution
Each zero is formed on multiplying by 10. Prime factorisation of 10 is 2 5. So no. of 0's depends on number of 2's and 5's. There will be more 2's while multiplying 100!, so we can just count the 5's. We get 20 5's from multiples of 6 from 1-100, but 25 gives us 2 5's to multiply with and form 0's. So for every multiple of 25, we add 1 more 5. So we add 4 more 5's(25,50,75,100). Since there are no multiples of 5 5*5(125), we can stop here. 20+4=24, meaning that in 100!, 5 will get multiplied 24 times, no more. There will obviously be atleast 24 2's. Therefore each of these 5's will multpily with a 2 to give us 24 trailing 0's