What is the last two digit of 173^2365?

• 173^2365
  =>173*173^2364
  =>173*(173^4)^591 {173^4 = 895745041}
  =>173*(...41)^591 last two digit of {..a1}^..pq = a*q*10+1
  =>173*(...41)
  =>..73*...41
  =>....93
  Ans :- the last two digits are 93
• 11 years agoHelpfull: Yes(5) No(0)
• It's 93
  
  173^2365 is same as 73^2365
  
  Also last two digits of 73^20 = 01
  => 73^2360 = 01
  => 73^2360 x 73^5 = 73^5 x 1 = 93
  
• 11 years agoHelpfull: Yes(1) No(0)
• 3^5=243.........last 2 digits 43
• 11 years agoHelpfull: Yes(0) No(3)
• we know that (abc)^pqr if c=1 then last two digit is (b*r,1)
  so 73^2365 = 73. 73^2364 = our aim to make 1st digit 1
  now 73.(73^4)^591 = 73.(41)^591 = hence 73*41 = 93 Ans
• 11 years agoHelpfull: Yes(0) No(0)