what is the highest power of 3 available in the expression 58!-38!
1.17
2.18
3.19
4.none

• 1.17
  
  58!-38!= 38!*( 58!/38! -1)
  
  Here 38! is multiple of 3 whereas ( 58!/38! -1) is not a multiple of 3.
  Now 38! is having 17 as highest power of 3.
  3,6,12,15,21,24,30,33..1 power each......... total 8
  9,18,36 ----- 2 powers each.................. total 6
  27 ........... 3 powers...........................3
  
  Sum total =17
  
  
• 12 years agoHelpfull: Yes(9) No(4)
• Answer: 17
  
  highest power of 3 available in above expression is max number of 3s in 38! = 17
• 12 years agoHelpfull: Yes(7) No(6)
• 4. None
  
  58!-38! = 20!
  
  As per the given Option,
  
  3^17 = 129140163(Carry 9 digits)
  3^18 = 387420289(Carry 9 digits)
  3^19 = 1162261467(Carry 10 digits)
  
  20! = 20*19*18*17*16*15*......*3*2*1
  
  20*19*18*17*16*15*14 = 390700800(Carry 9 digits)
  20*19*18*17*16*15*14*13 = 5079110400(Carry 10 digits)
  
  So, No maximum power of 3 as per the Options in given expression.
  
  Answer = Option 4.None
• 12 years agoHelpfull: Yes(0) No(15)