Latest TCS Aptitude Question SOLUTION: N! have 37 zeroes at its end. How many values of N are possible?

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N! have 37 zeroes at its end. How many values of N are possible?

Asked In TCS utkarsh bisht (10 years ago)

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Palash Bansal  (10 years ago)

0 can come in the end only of no. ends with 0 or 2 no.s ending with 2 and 5..which on multiplying give one 0.
So, we have to count no. of 0's,2's and 5's
As a combination of 2 & 5 gives a 0..but there are less no. of 5's as compare to 2's
therefore, we now only want to count no. of 0's and 5's
Special cases-
{ Note-25 and 75 gives 2 5's each
Similarly, 125 gives 3
& 100 gives 2 0's
take care of this..dont forget to count..
}
Now, 1-150 has ~15~ 0's in 10,20,30,...,150
& 1-150 has ~15~ 5's from 5,15,25,35,...,145
Special cases-
~1~ more 0 from 100
~2~ more 5's from 25,75,, ~2~ 5's from 50,150 and ~2~ more 5's from 125
Total = 15+15+1+2+2+2=37
So, N=150 and also 151,152,153,154 coz these 4 following no.s doesn't give any 0 or 5..but 155 does..
THIS CONCEPT IS USED FOR ANY QUESTION OF COUNTING ZEROES IN FACTORIAL, and we use symmetry of special cases..25,125,625..100,1000...to calculate faster :)

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poulomi roy  (10 years ago)

150,151,153,154 will be the answer

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Palash Bansal  (10 years ago)

sry all..this previous answer of mine is incorrect
Poulomi roy is right..
adding to my answer that 150,151,152,153,154 will give 37 0's
so total no.s are 5
therefore N=5 is the answer
Note: any question of this type always has answer=5 as after every 5 no.s, no. of 5 increases and hence no. of zeroes by 1 if no. is small 2 if large and so on...
my previous solution is used to calculate no. of zeroes dat is xactly reverse of question above
ALSO ITS A TIME CONSUMING METHOD
So, iff question comes as "find no. of zeros" then use trick mentioned below..
N/(5^1)+N/(5^2)+N/(5^3)+..
divide and ignore remaider whatever comes
Example- find no. of zeroes in 1040! ???
Solution- 1040/5+1040/25+1040/125+1040+625 next power of 5 > 1040 so leave it here
1040/5+1040/25+1040/125+1040+625 = 208+41+8+1 = 258
I just read this trick from wikipedia
http://en.wikipedia.org/wiki/Trailing_zero

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Karthika  (10 years ago)

@Palash: what is its asked how many 12's are there in 100!? we were asked a qn like that in our placement program! can u plz help

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Karthika  (10 years ago)

Hey poulomi,can yu please explain it in detail??

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Karthika  (10 years ago)

Thankyou Palash! Understud it very clearly!

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