12341234.... 400 digits when divided by 909 leaves remainder ?

• Ans: 685
  The pattern repeats by four digits 1234!
  First find the "pattern base" = 1234 (In our case!)
  Then find 1234 mod 909 = 325
  Now if you see 12341234 mod 909 = 325*2 mod 909 = 650
  Again observe for 123412341234 mod 909 = 325*3 mod 909 = 66 and so on
  So, we have 100 such "pattern base" 1234
  Therefore, remainder will be given by 325*100 mod 909 = 685.
  
• 11 years agoHelpfull: Yes(34) No(2)
• Ans: 685
  The pattern repeats by four digits 1234!
  First find the "pattern base" = 1234 (In our case!)
  Then find 1234 mod 909 = 325
• 11 years agoHelpfull: Yes(2) No(4)
• 1234/909 leaves remainder 325
  12341234/909 leaves remainder 650
  123412341234/909 leaves remainder 0
  similarly 1234123412341234/909 leaves 0 remainder
  hence 1234 upto 400 digits will leave 0 remainder
• 11 years agoHelpfull: Yes(1) No(3)
• 1234/909 leaves remainder 325
  12341234/909 leaves remainder 650
  123412341234 mod 909 leaves remainder 0
  but this continues until 123412341234.......1234(99 times) mod 909 leaves remainder 0
  therefore for 100th time we need to calculate
  so 1234 mod 909=325
  so answer is 325
• 11 years agoHelpfull: Yes(0) No(1)