Find the number of powers of 20 in 100!
(a) 24 (b) 12 (b)1 (d)55

• it will be 24.
• 12 years agoHelpfull: Yes(10) No(1)
• Power of a prime p in a factorial (n!)
  
  
  
  
  The biggest power of a prime p that divides n! (or in other words, the power of prime p in n!) is given by the sum of quotients obtained by successive division of n by p.
  
  
  
  
  Example: What is the highest power of 7 that divides 1342!
  
  
  ? [1342 / 7] = 191
  
  
  ? [191 / 7] = 27
  
  
  ? [27 / 7] = 3
  
  
  ? Power of 7 = 191 + 27 + 3 = 221
  
  
  
  Example: What is the highest power of 6 that divides 134! ?
  
  
  As 6 is not a prime number, we will divide it into its prime factors. 3 is the bigger prime, so its power will be the limiting factor. Hence, we need to find out the power of 3 in 134!
  
  
  ? [134/3] = 44
  
  
  ? [44/3] = 14
  
  
  ? [14/3] = 4
  
  
  ? [4/3] = 1
  
  
  ? Power of 3 in 134! = 44 + 14 + 4 + 1 = 63
  
  
  
  Example: What is the highest power of 9 that divides 134! ?
  
  
  As 9 is not a prime number, we will divide it into its prime factors. 9 is actually 32. The number of 3s available is 63, so the number of 9s available will be [63/2] = 31.
  
  
  Highest power of 9 that divides 134! is 31.
  
  
  
  Highest power of 18 and 36 will also be 31. Highest power of 27 will be [63/3] = 21.
  
  
  
  Note: To find out the highest power of a composite number, always try and find out which number (or prime number) will become the limiting factor. Use that to calculate your answer. In most cases you can just look at a number and say that which one of its prime factors will be the limiting factor. If it is not obvious, then you may need to find it out for two of the prime factors. The above method can be used for doing the same.
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  by using this we get 24 :)
• 12 years agoHelpfull: Yes(8) No(0)
• @pulkit -24 will be the total no of zeros at the and of 100!...
• 12 years agoHelpfull: Yes(1) No(0)
• sry friends answer will be 24
• 12 years agoHelpfull: Yes(1) No(0)
• plz explain ?????????
  
• 12 years agoHelpfull: Yes(1) No(0)
• TARUN SAI thanks for giving such good explanation
• 12 years agoHelpfull: Yes(1) No(0)
• answer will be 20 which is not given in option am i correct ??????
• 12 years agoHelpfull: Yes(0) No(5)
• answer will be 24..
• 12 years agoHelpfull: Yes(0) No(0)