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zeroes in 100!

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zeroes in 100!

by ruplun » Thu Feb 23, 2012 8:45 am
How many zeros does 100! end with?

(A) 20
(B) 24
(C) 25
(D) 30
(E) 32

Can u please expalin in detail the logic behind this ...
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by kul512 » Thu Feb 23, 2012 10:08 am
Number is zeros in n is-

(n/5)+(n/25)+(n/125)...

if n=100
(100/5)+(100/25)=20+4=24

Logic is: Number of zeros means total number of 10. Total number of 10 means total number of 5 (because 2 is available in abundant :-)). To calculate the number of 5 we divide 100 by 5, first term of the above written expression. But four terms are there which have 2 five embed in them and they are 25,50,75,100 so total 4, which is second term of the above written equation.
Answer is B.
Last edited by kul512 on Thu Feb 23, 2012 5:11 pm, edited 1 time in total.
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by neelgandham » Thu Feb 23, 2012 1:19 pm
100! = 1*2*3*4*5*...10...15...20...25....100 = (5^n) * X, where X,n are integers

The Total number of zeroes = Total number of 5's in the product.

First method - Counting the number of 5's
5 - 1,
10 - 2,
15 - 3,
20 - 4
25(5*5) - 5,6
30 - 7,
35 - 8,
40 - 9,
45 - 10,
50(5*5*2) - 11,12,
55 - 13,
60 - 14,
65 - 15,
70 - 16,
75(5*5*3)- 17,18,
80 - 19,
85 - 20,
90 - 21,
95 - 22,
100(5*5*4) - 23,24

Total - 24

Second Method - Mentioned above by kul
Anil Gandham
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