what is the remainder when 72^21 divided by 25

• Sorry ans. 22 will be correct
  (75-3)^21-->(-3)^21-->(-27)^7-->(-2)^7
  So -128/25 remainder -3 or 22 ans
• 9 years agoHelpfull: Yes(38) No(8)
• Ans:2
  72^21 mod 25
  unit digit is 2
  2^n unit digits on 2,4,8,6,2,4,8,6....
  21/4=remainder 1
  1st place unit digit is 2 so 2 mod 25 is 2 Ans..
• 9 years agoHelpfull: Yes(16) No(24)
• 72^21/25
  
  =72/25 ^ 21/20 (bcz 25 is not prime no. so, Qn= 25(1-1/5)=20)
  =22^1
  ans=22 remainder
• 9 years agoHelpfull: Yes(9) No(1)
• 72^21/25 can be written as
  (25*3-3)^21/25
  so -3^21 is odd term in that case
  remainder will be 25-3=22
  rem=22
• 9 years agoHelpfull: Yes(8) No(1)
• using -ve remainder theorm
  (-3)^21/25=-(2)^7/25=-3/25=22
• 9 years agoHelpfull: Yes(5) No(1)
• @suraj jha nope..preparing for apti:D
  @raviteja..i dint get yur question
• 9 years agoHelpfull: Yes(3) No(1)
• (70+2)^21 since 70 is divided by 5 take now 2^21=2097152/5 so answer is 4
• 9 years agoHelpfull: Yes(2) No(7)
• 72/25 gives remaimder 22 ,and {(22*22*22)^7} gives remainder -2 and (-2)^7/25 gives remainder -3 , as we know remainder can,t be negative , so answer will be -3+25=22 ans
• 9 years agoHelpfull: Yes(2) No(0)
• 72^21/25
  (75-3)^21/25
  (-3)21=cycl reminder unit digits 3,9,7,3,9,7,3,9,7...upto 21
  21/3=7
  7th place unit digit is 3
  So the ans is -3 or 3 or 22....
  best way is take option to..
• 9 years agoHelpfull: Yes(2) No(3)
• consider last digit i.e.2 so 2^21=2
  so 2/25=>rem=2
  
• 9 years agoHelpfull: Yes(1) No(7)
• have u appeared for tcs apti...@divya
• 9 years agoHelpfull: Yes(1) No(2)
• why u have written 25 @divyapatel
• 9 years agoHelpfull: Yes(1) No(2)
• 10 Ans
  72^21/5
  -->(70+2)^21-->2^21-->(5-1)^10 *2-->(-1)^10 *2-->2
  So 2/5 remainder=2
  So (2/5)*(5/5)=10/25 remainder is 10
• 9 years agoHelpfull: Yes(1) No(1)
• 2^1=2
  2^2=4
  2^3=8
  2^4=16
  2^5=32
  cyclicity of 2 is 4
  so divide the power with 4
  remainder is 1
  then 2^1=2
  so 2%25=2
  ans is 2
• 9 years agoHelpfull: Yes(1) No(3)
• wt's d crct ans amomg those
  
• 9 years agoHelpfull: Yes(1) No(0)
• 72^21--->(75-3)^21 since 75 is completely divisible by 25 now
  (-3)^21 ---> (-3) which means the remainder is 25 - 3 = 22 ans.
• 9 years agoHelpfull: Yes(1) No(1)
• 72/25=22(remainder)
  22/25=22
  (22^2)/25=9
  (22^3)/25=23
  (22^4)/25=1
  our objective is to achieve 1 as remainder. so we get in 4th term. our cycle is 4.
  now
  21/4=1 remainder.
  we got in 1 the remainder is 22.ans
• 9 years agoHelpfull: Yes(1) No(0)
• Ans. 24
  (24-(-1))=25
  72 is divisible by 24 and -1^21=-1
  now add this to divisor 25+(-1)=24
  
• 9 years agoHelpfull: Yes(0) No(2)
• @ Mounika
  No doubt 22 is correct ans
• 9 years agoHelpfull: Yes(0) No(0)
• 7
  answer is 7
• 9 years agoHelpfull: Yes(0) No(1)
• ans is 22
  (72)^21/25 remainder is -3
  then (-3)^21/25 to form a 25 group we need more 22 numbers so remainder is 22
• 9 years agoHelpfull: Yes(0) No(1)
• 12we get remainder 12
  
• 8 years agoHelpfull: Yes(0) No(1)
• we have to know the distance first
• 7 years agoHelpfull: Yes(0) No(0)