HOW MANY POWERS OF 20 ARE THERE IN 100! ??

• 24 will be the correct answer
  
  20 = 5*4 = 5*2*2
  
  now [100/5] + [100/5^2] = 20 + 4 = 24(power of 5 is 24)
  
  now [100/2] + [100/2^2] + [100/2^3] + [100/2^4] + [100/2^5] + [100/2^6] =
  
  50 + 25 + 12 + 5 + 3 + 1 = 96
  
  Power of 2 is 96*2 = 192 (because we have two 2)
  
  so power of 4 will be 192/2 = 96
  
  but we have only 24 power of 5 so we will take only 24 power of 4 instead of 96
• 11 years agoHelpfull: Yes(12) No(9)
• firstly we ll find out the prime factor of 20 and the factor of 20 is 2 and 5
  because ,
  
  20=2*2*5
  
  now we just need to find out how many power of 5 are divisible by 100!
  
  so 100/5= 20
  and 100/5^2=100/25=4
  100/5^3=100/125 =0 we are counting just integer values on decimal
  
  adding both value we will get 24
  and this is the answer
  
  in such typ of question we just need to divide the num by given number's highest prime factor . :)
• 11 years agoHelpfull: Yes(5) No(0)
• 24 will be the correct answer
  
  20 = 5*4 = 5*2*2
  
  there fore [100/5]+[100/25]= 20 + 4 = 24
  similarly for 2
  
  [100/2]+[100/4]+[100/8]+[100/16]+[100/32]+[100/64]= 50+25+12.5+6.25+3.125+1.5625= it comes around 98
  
  so now we want it for 4 so 98/2= around 49
  
  so foe powers of 20 we have to take common
  like we have 24 (5 powers)and 49(4 powers)
  common we take 24 (5*4=20 powers)
  
  so ans is 24
• 11 years agoHelpfull: Yes(2) No(0)
• 20 appears in 20,40,60,80,100(5 times here) in addition to that 20 can be expressed as (5*4) or (2*10).so we have to count the no. of 5's appearing in 100! excluding the above 5 numbers.5 appears once in 5,15,30,35,45,55,70,85,90,95(10 times here) and twice in 25,50,75(6 times here).so total power of 20 in 100! is 5+10+6=21
• 11 years agoHelpfull: Yes(1) No(1)
• only 2
  i.e 20^0,20^1
• 11 years agoHelpfull: Yes(1) No(2)
• 5 = 100/20 = 5
• 11 years agoHelpfull: Yes(0) No(3)