Question

How many zeros are there at the end of 100.Explain clearly.

Answer 1

First of all its 100! not just 100 in the question otherwise it will be irrelevant..

now,

100! = 1 x 2 x 3 x 4 x 5 6 x 7 x 8 x 9 x 10 x ---- x 15 x 20 x ----- 90 x ---- x 95 x----x 100 .

SI, 11 zeroes we get from numbers such as 10,20,30,...........,90,100)

now a zero can be added if we have a 2 and a 5 i.e, 2 x 5 = 10.

how many such 2s & 5s we get -
between 1 to 10 we get one set of 2 & 5.
similarly we get one set each - from 11 to 20, from 31 to 40, from 51 to 60, from 61 to 70, from 81 to 90 & from 91 to 10.
total 7 such sets or 7 zeroes can be added.

now 21 to 30, 41 to 50 & 71 to 80 are different.
from 21 to 30 we get two 5s from 25. hence we will get two sets of 2 & 5.
from 41 to 50 we get one 5 from 45 & one more 5 from 50. hence we get two sets of 2 & 5.
from 71 to 80 we get two 5s from 75 or 5 x 5 x 3. hence we get two sets of 2 & 5.
total 6 sets or 6 zeroes can be added.

hence total no of zeroes = 11 + 7 + 6 = 24.