what is the last two digits of 123^123!

• 123! will have more than 2 zero at the end, so it is a multiple of 4.
  
  Now (123^4)^(...00)
  =(228886641)^(...00)
  Now powers of 41 repeat the last two digits.
  ie 41^1=41 41^6=..41
  41^2=..81 41^7=..81
  41^3=..21 41^8=..21
  41^4=..61 41^9=..61
  41^5=..01 41^10=..01
  
  As 123! will still be having some zeroes left at the end so it value is a multiple of 10 and so the last 2 digits are 01.
• 11 years agoHelpfull: Yes(45) No(7)
• bt 123! is on the power,so how it will be 00 ?? @Piyush
  
• 11 years agoHelpfull: Yes(18) No(3)
• it is in the form
  (123)^(x0000..(28 zeros))
  =>((123)^4)^(y000..)
  => (z41)^(y00..)
  =>units place=1,tens place=4*0=0
  =>last two digits=01.
  
  last two digits will be 01
• 11 years agoHelpfull: Yes(11) No(7)
• The last two digits should be 00 because on calculating the factorial of 123, we have 1 * 2 * 3 * ....... * 123, so we get 2 * 5 and 10 also in between so their product is 100 whatever else multiplied the last two digits will be 00 only.
• 11 years agoHelpfull: Yes(9) No(18)
• mr.asit shukla....can u elaborate the soln...so that it becomes more clear..
  
• 11 years agoHelpfull: Yes(5) No(1)
• last 2 digits of any no. A^(40k+r) = A^r...
  in this case 123^123= 123^((40*3)+3)= 123^3 = 67
• 11 years agoHelpfull: Yes(5) No(3)
• mr. asit shukla can u please elaborate more esailyyy
• 11 years agoHelpfull: Yes(4) No(3)
• the last digit will be 9 bt dono about last but one digit
• 11 years agoHelpfull: Yes(3) No(10)
• last two digits will be 01
• 11 years agoHelpfull: Yes(2) No(1)
• 01 will be the last two digits !!!
• 11 years agoHelpfull: Yes(2) No(0)
• as 123! will be divided by 4. So (123^4)^(.......00) because 123! will have atleast two zeroes in the end digits.
  Now 123^4=228886641.Here 41 is the last two digits as
  228886641^(.............00)
  So by checking the power cycle of 41,
  41^1=41
  41^2=81(note:we are checking only last two digits so only last two digts i am writing)
  41^3=21
  41^4=61
  41^5=01
  and 41^6=41 from this stage the last two digits starts repeating itself.
  So the last two digits are 01.
• 10 years agoHelpfull: Yes(1) No(1)