what is the remainder when 7^700 is divided by 100?

• ans will be 1..
  as when 7^1 is divided by 100,denremainder ll be 7..wen 7^2 is divided by 100,den rem-49..wen 7^3--rem will be 43..wen 7^4 --rem will be 1..wen 7^5--rem will be 7..wen 7^6--rem will be 49..if u ll go on checking like the other powers..u ll find after 7^4 its repeating...ques is to find out 7^100..so of u ll take the ramainder as a pair of 4(7,49,43,1)..den u cn get remainder will be 1 for 100
• 12 years agoHelpfull: Yes(15) No(1)
• (7^700)mod100= [7^(2*350)]mod100=[49^350]mod100=[(50-1)^350]mod100=[{350C349}*50*(-1)^349 +350C350*(-1)^350]mod100 = [-350*50+1]mod100=1mod100
  So, evidently, the remainder will be 1.
• 12 years agoHelpfull: Yes(6) No(0)
• 7^700 = (7^4)^ 175 = (2401)^175
  this number has last two digits 01. So when divided by 100, it will give reminder as 1.
  
  
• 12 years agoHelpfull: Yes(4) No(0)
• 49..7^1/100=7
  7^2/100=49
  7^3/100=43
  7^4/100=1
  cycle repeats..so 700/4=2
  49
• 12 years agoHelpfull: Yes(3) No(0)
• 43.
  7^0/100=1
  7^1/100=7
  7^2/100=49
  7^3/100=43
  ..
  7^7/100=43..
  similarly.....
  7^7/100=43
• 12 years agoHelpfull: Yes(3) No(2)
• 7^4/100 will give 1 remainder...so 700/4=0.
  so remainder will be=1.
• 12 years agoHelpfull: Yes(1) No(0)
• @teja .. your solution is helpful , but got stuck up at the end.. how can I be sure that 700 is in that position? You've given 700/4=2. how can it be when 700/4=175.
• 12 years agoHelpfull: Yes(0) No(1)
• yes..i was mistaken at the end..may b remainder is 1
• 12 years agoHelpfull: Yes(0) No(0)
• still confused..
• 12 years agoHelpfull: Yes(0) No(1)
• any methods to solve these remainder type questions ??
• 12 years agoHelpfull: Yes(0) No(1)