what is the reminder when 7^7oo is divided by 100?

options:
(a)1 (b)41 (c)41 (d)21

• 1 is the answer...as u can check that 7^1=7,7^2=9(units plc),7^3=3(unit plc),7^4=1 and 7^5=again 7 at unit's plc... so variation is after 4powers...so divide the power by 4 n c what remaindr it gives...700/4=175 no remaindr...so it will end upto 4powers...so value of the 4th power is 1... n so when 100 will divide it it will give 1as its remainder...
• 12 years agoHelpfull: Yes(7) No(0)
• answer : 1
  explanation:
  7^700 can be written as..(7^4)^175=(2400+1)^175
  as we know ,if we expand this by binomial theorem we have each term except last is divisible by 100 ....hence remainder is last term i.e 1^175.
  so answer is 1.
• 12 years agoHelpfull: Yes(3) No(0)
• 7^4=2401 and 7^700=(7^4)^175
  so rem =1*1*...175 times=1
• 12 years agoHelpfull: Yes(3) No(0)
• 7^700 mod 100
  [(((7)^3)^233).(7)^1] mod 100
  [((343)^233) .7] mod 100
  (100*3+43)^233 .7 mod 100
  (43)^243 .7 mod 100
  now we take only (43)^243 .7mod (10*10)
  so first (43)^243 .7 mod 10
  (10*4+3)^243 .7 mod 10
  3^243 .7 mod 10
  27^81 .7 mod 10
  (10*2+7)^81 .7 mod 10
  7^81 mod 10
  (7^2)^40.7.7 mod 10
  (49)^40 .49 mod 10
  (10*4+9)^40 .49 mod 10
  (9)^40 .49 mod 10
  (10-1)^40.49 mod 10
  (-1)^40 .49 m0d 10
  so it will be 1*49=49
  so we 49 mod 10=9
  so 9 will be remainder when 7^7oo is divided by 100
• 12 years agoHelpfull: Yes(2) No(4)
• 7^700=(7^4)^28...
  7^4 %100=1
  =>(7^4)^28 %100 =1^28 %100
  =1;
• 12 years agoHelpfull: Yes(0) No(1)