Latest TCS Aptitude Question SOLUTION: how many sero's r dere in 100! ?

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(#M40012713) TCS question Keep an EYE

how many sero's r dere in 100! ?

Asked In TCS aanchal kushwaha (12 years ago)

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venkatrao  (12 years ago)

counting number of zeros at the end of n!
value will be
n/5 + n/5^2 + n/5^3 + n/5^4 + ..........
the integral value of this sum will be the total number of zeros.
in this question n=100
100/5 + 100/5^2 + .......
the integral value is 20+4=24.

Is this solution Helpfull? Yes (37) | No   

rocks  (12 years ago)

100/5=20
20/5=4
20+4=24

Is this solution Helpfull? Yes (11) | No (1)  

Kamakshi  (12 years ago)

We need to look at the prime factors that make up 100!. Each time we multiply a factor of 2 and a factor of 5 together we get 10, which adds a zero. Obviously there are more factors of 2 than 5. So the answer to the question is to find the number of factors of 5.

Every fifth number starting with 5 has a factor of 5, for a total of 100/5 = 20.

Every twenty-fifth number starting with 25 has a second factor of 5, for a total of
100/25 = 24.

So the total number of factors of 5, and hence the number of zeros at the end is:

20 + 4 = 24

Is this solution Helpfull? Yes (10) | No   

rahul  (12 years ago)

counting number of zeros at the end of n!
value will be
n/5 + n/5^2 + n/5^3 + n/5^4 + ..........
the integral value of this sum will be the total number of zeros.
in this question n=100
100/5 + 100/5^2 + 100/5^3 + .......
the integral value is 20+4=24.

Is this solution Helpfull? Yes (4) | No   

meena n  (12 years ago)

24?
divide 100 by 5, and then add last two quotients

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snehil  (12 years ago)

no sero will be there :)
but 24 zeros will be there

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Keshav Gupta  (12 years ago)

100/5=20 AND 100/25=4
THAN 20+4=24.

Is this solution Helpfull? Yes (3) | No   

Ankesh Srivastava  (12 years ago)

it is lyk
100/5=20
100/25=4
now value of 5^3 exceeds 100 so no further calculation
ans is =20+4=24

Is this solution Helpfull? Yes (2) | No   

venkat mani  (12 years ago)

Let’s 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. For people who like to look at it from a formula point of view

Number of 5′s = 100/5 + 100/25 + 100/125 + … = 24
so the toatal num of 2's is 97 in 100!
now multipling wit 5*2 we'll get 0
total 24 pairs are der so the answer is 24

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ANSHU KUMAR  (12 years ago)

(100/5)+(100/5^2)=24

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