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

• ans is a) 24
  20 is = 4*5 = 2^2 * 5
  so we will look for no. of 2's and 5's in 100!.
  no of 5's are= 24
  np of 2's are=97, np of 4's are = 48
  restrcting to the smaller quantity ans :24
• 12 years agoHelpfull: Yes(19) No(4)
• Keep on dividing 100 by 2.. find the maximum power of 2 in 100!
  100/2=50, 50/2=25, 25/2= 12, 12/2=6, 6/2=3, 3/2=1, therefore total=50+25+12+6+3+1=97
  Similarly for power of 5
  100/5=20, 20/5=4 total=20+4=24
  now factors of 20= 2*2*55
  Power of 5=24, Power of 2=24+24=48
  Therefore, power of 20=24
• 12 years agoHelpfull: Yes(7) No(1)
• 20 = 5 * 4
  thus the no. of times 5 & 4 will appear in 100! will be the power of 20 in 100!..
  but it is well understood that no. of 5's are always lesser than 4 in 100! ...
  thus we only need to calculate no. of 5's...
  = (100/5)+(100/25)
  =20+4
  =24 is d power of 20.
• 12 years agoHelpfull: Yes(3) No(1)
• Explain Properly.......I didn't understand...!
• 12 years agoHelpfull: Yes(2) No(3)
• Plzzz xplain !!!
  
• 12 years agoHelpfull: Yes(2) No(3)
• itz not just 100..itz 100 factorial(100!).
• 12 years agoHelpfull: Yes(2) No(0)