Guyz i am unable yo understand remainder theorem..plz help me ..how to find remainder when 59^28 is dived by 7...similary 67^99 is divided 7...plz explain in detail...i need it...

• 67^99 can be written as (63+4)^99 which divided by 7gives 4^99....
  4^99can be writtn as 4^3*33=64^33 and 64 can be written 63+1^33/7=1^33
  1^33/7 so remainder is 1
  according to me both question remainder is 1
  
  
  
• 9 years agoHelpfull: Yes(6) No(0)
• 59^28 can be written as (56+3)^28 which divided by 7 gives 3^28 as remainder...
  3^28 can be written as 27^9 *3 = (28-1)^9*3 which divided by 7 gives (-1)^9*3 as remainder.
  so,(-1)^9*3=-3 can be written as (-7+4) which divided by 7 gives 4. so remainder is 4.
• 9 years agoHelpfull: Yes(1) No(0)
• you can be write 59^28 as (56+3)^28 ,56 is divisible by 7 then we can be write 3^28 as reminder...
  3^28=now we can be write ((3^5)^5)*3^3.......3^5 =343 which is divisible by 7 then we can simply write..1^5*3^3=1*3*3*3=27..then we get reminder 6
• 9 years agoHelpfull: Yes(1) No(0)
• Watch videos on YouTube by takshzilla shikshak first.. U won't feel any difficulty after that
• 9 years agoHelpfull: Yes(1) No(0)
• in 59^28, take unit digit of 59 which is 9..
  the repetitive squence of 9 is:
  9^1=9
  9^2=81
  9^3=729 nd so on..
  if yu observe the unit's digit in this sequence , it turns out to be 9,1,9,1,etc..(two numbers)
  
  so divide 28 by 2.. remainder is 0
  9 can be taken for odd remainders, 1 for even remainders..
  since 0 is even we can take 1..
  1 divided by 7.. remainder is 1.. ans is 1
  hope you get me..
  
• 9 years agoHelpfull: Yes(0) No(1)
• according to me
  ans is1
  
• 8 years agoHelpfull: Yes(0) No(0)
• please see the video of dinesh mirglani remainder chapter video yuour concept will be clear
• 8 years agoHelpfull: Yes(0) No(0)
• 59^28
  59 % 7 = 3
  Hence the problem is converted into 3 ^ 28
  7 ^ 1 =7
  7 ^ 2 = 49
  7 ^ 3 = 343
  7 ^ 4 = 2301
  7 ^ 5 = 16107
  cycle is of 4
  28 % 7 =0
  Hence rem = 1.
• 8 years agoHelpfull: Yes(0) No(0)
• 59^28/7 can be written as (56+3)/7 which is {(7n+x)/7 = x/7}; 3^28 /7.....deduce until (7n+1)/7=1 or x/7(x
• 8 years agoHelpfull: Yes(0) No(0)