when a certain number x is multiplied by18,the product y has all digits as 4s.what is the minimum number of digits x can have?

• x*18=444....
  x=(444....)/18
  x=(222....)/9
  
  we know that any no. is divisible by 9 only when sum of all its digit is divisible by 9
  so
  2+2+2...9times=18 which is divisible by 9
  so
  x=222222222
  so there r 9 digits in x
• 12 years agoHelpfull: Yes(34) No(14)
• 222222222*18=3999999996
  it is not equal to 4444....
  as the qstn is 'minimum' no of digits.
  ans is 8 digits and the no is 24691358
• 11 years agoHelpfull: Yes(23) No(9)
• 9 digits
  so that sum of digits is divisible by 9.
• 12 years agoHelpfull: Yes(3) No(12)
• Its simple....
  4444444444...... / 18. Go on divide until U get reminder 0. When U get reminder 0. Stop and note down the total number of digits in the answer
• 10 years agoHelpfull: Yes(3) No(3)
• 9 digits is the answer,but how??plz elaborate..
• 12 years agoHelpfull: Yes(1) No(7)
• here its asked how many digits can x have??so,18*8digits=all 4's. number of 4's are 9.
• 12 years agoHelpfull: Yes(1) No(6)
• 24691358 is the number and it has 8 digits.
• 10 years agoHelpfull: Yes(0) No(1)
• Good explanation SIDDARTHA. Thanx
• 9 years agoHelpfull: Yes(0) No(1)
• Digit 444444444...n is written as 4 (10^n-1)/9 so 18 x = 4( 10 ^n-1)/9 So n will be 9 . So digit of x will be 1 less than of 4444 number that is 8
• 8 years agoHelpfull: Yes(0) No(0)
• FIRST METHOD to solve :
  
  x= 444444..... / 18
  x= 22222..... / 9
  sum of the digits should be divisible by 9.
  so 2+2+2....(9times) =18 which is divisible by 9.
  (Since 2 is less than 9 therefore, 22 will be the first no. to be divided by 9. Thus deducting one 2 from 9
  2s. i.e 9-1=8 )
  so there are 8 minimum digits.
  and the number will come out to be 24691358.
  24691358 * 18 = 444444444.
  
  
  SECOND METHOD
  to solve this is keep on dividing 444.... by 18 unless the remainder comes out to be 0. The quotient will be our x . x=24691358
  Count the number of digits that is our answer i.e 8.
  24691358 * 18 = 444444444
• 6 years agoHelpfull: Yes(0) No(1)