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

• 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 :)
• 11 years agoHelpfull: Yes(11) No(0)
• 150,151,153,154 will be the answer
  
• 11 years agoHelpfull: Yes(4) No(1)
• 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
• 11 years agoHelpfull: Yes(2) No(0)
• @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
• 11 years agoHelpfull: Yes(1) No(0)
• Hey poulomi,can yu please explain it in detail??
• 11 years agoHelpfull: Yes(0) No(0)
• Thankyou Palash! Understud it very clearly!
• 11 years agoHelpfull: Yes(0) No(0)