What is the last two digit of 74^2365?

• last 2 digits of 74^1=74
  last 2 digits of 74^2= 76... from 5476
  last 2 digits of 74^3= 24 ...... from 405224
  last 2 digits of 74^4= 76... from 5476
  last 2 digits of 74^5= 24
  
  
  so last 2 digits of 74^(2n)= 76... from 5476
  last 2 digits of 74^(2n+1)= 24
  
  so last two digit of 74^2365 will be 24.
  
• 12 years agoHelpfull: Yes(8) No(0)
• 74^2 = 5476
  76^n has last two digits = 76
  => 74^(2 x 1182) = 76^(1182) = 76
  74^(2364) x 74 = 76 x 74 = 24
  => last two digits = 24
  
  You can also apply congruency method.
  74^2 ≡ 76 (mod 100)
  (74^2)^1182 ≡ 76^1182 ≡ 76 (mod 100)
  (74^2364)x 74 ≡ 76 x 74 ≡ 24 (mod 100)
  => last two digits = 24
  
• 12 years agoHelpfull: Yes(0) No(1)
• 74^2365
  ans.24
  Take 4^5=1024. separate 4 from it
  Now, multiply 7 with 6 i.e., 42.
  from 42 take 2 and place it before 4, which we already get.
  so, final ans 24
  
  
• 11 years agoHelpfull: Yes(0) No(0)