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(#M40026403) TCS question Keep an EYE

find the numbers of zeros at the end of 100!

Asked In TCS javed saifi (11 years ago)

Solved Upasana Rai Read Solution (11)

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Upasana Rai  (11 years ago)

count the number of 5′s and 2′s in the multiplication.
count the 5′s first. 5, 10, 15, 20, 25 and so on making a total of 20. However there is more to this. Since 25, 50, 75 and 100 have two 5′s in each of them (25 = 5 * 5, 50 = 2 * 5 * 5, …), you have to count them twice. This makes the grand total 24.
Formula point of view-
Number of 5′s = 100/5 + 100/25 + 100/125 + … = 24 (Integer values only)
similarly,count the number of 2′s. 2, 4, 6, 8, 10 and so on. Total of 50 multiples
Since we have only 24 5′s, we can only make 24 pairs of 2′s and 5′s thus the number of zeros in 100!is 24.

Is this solution Helpfull? Yes (45) | No (1)  

prayas goel  (11 years ago)

100/5=20
20/5=4
again 4 can not be divisible by 5
So, 20+4=24 zeros

Is this solution Helpfull? Yes (37) | No (5)  

Guru Pranav  (11 years ago)

100/5=20,
20/5=4
20+4=24.
24 0's are there

Is this solution Helpfull? Yes (9) | No (3)  

pranay sharma  (11 years ago)

dividing with 5 we get zero,
1. 100/5=20
2. den 5^2=25 so ,100/25=4
3. den 5^3=125 , but we want to find till 100! den adding .
ans-20+4=24.

Is this solution Helpfull? Yes (7) | No   

prayas goel  (11 years ago)

24 zeros at the end of 100!

Is this solution Helpfull? Yes (6) | No (2)  

pratik jitendra malviya  (11 years ago)

for finding zero's in factorial we have to divide that no. by 5 and add the remainder so(100/5+20/5+4/5)=20+4+0=24

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Sahil  (11 years ago)

24 zeros...

Is this solution Helpfull? Yes (2) | No   

Avnish Thakur  (11 years ago)

100/5=20
20/5=4
4 can not be divisible by 5 that is remainder part end we get 0
So, 20+4=24 zeros

Is this solution Helpfull? Yes (1) | No   

tejomay saha  (11 years ago)

5*2=10 makes us 0 so there is process we have to repeatedly divide by 5 afterthat we have to add all the quotient. like in this case 20+4=24 zeroes will be there

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prafull mittal  (11 years ago)

u can simply calculate from 1-100 number who is taking aur making zero at end positions..

Is this solution Helpfull? Yes | No (8)  

Mallik konambhotla  (11 years ago)

to find number of zeroes.
let us consider 5 and 2
100/5+100/25=24
p(2)>p(5),so there are 24 zeroes in 100!

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