2^89/89 what will be the remainder?

• according to fermat's theorem : a^(p-1) mod p = 1 where p is a prime number
  thus we can write 2^89 as 2*2^88
  2*2^(89-1) mod 89 = (2 mod 89)*(2^(89-1) mod 89)
  =>2*1 = 2
  thus ans is 2
• 12 years agoHelpfull: Yes(15) No(0)
• ans will be 2.......
  we all know the power cycle of 4..
  so 89/4 we get 1
  so now 2^1/89
  then ans always 2..........
• 12 years agoHelpfull: Yes(13) No(6)
• remainder=2
  2 has the pattern pf 2,4,8,6,2 so,4n
  89/4=22+1
  so 2^1=2
  
• 12 years agoHelpfull: Yes(5) No(6)
• (2^9*2^9...upto 9 times*2^8)/89
  5*5*5*5*5*5*5*5*5*2/89
  125*125*250/89
  1*1*2=2 will be the remainder
• 12 years agoHelpfull: Yes(5) No(1)
• neeraj kumar pls explain in better way....
  and why did u divided 89 only by 4
• 12 years agoHelpfull: Yes(2) No(1)
• ans is 2...
• 12 years agoHelpfull: Yes(1) No(0)