when a certain number'x' is multiplied by 18, the product 'y' has all digit as 4s. what is the minimum number of digits 'x' can have?

• 18x = y
  
  All the digits of y are 4s
  18 = 9*2
  
  => to be divisible by 9,sum of all digits of y is divisible by 9
  => (4 + 4 + 4 + ...) is divisible by 9
  
  LCM of 9 and 4 is 36
  
  so there must be zero or nine 4s to be divisble by 18
  
  => 18x = (444...9 times) or 0
  => x = 0 or 24691358
  
• 12 years agoHelpfull: Yes(44) No(12)
• ans- 8
  just take a sequence of 4s ,lets start from two 4s and divide it by 18 and keep
  on adding number 4 in dividend and keep on dividing it till you get 0 as remainder.Count the digits of the quotient i.e. the answer.
  
• 12 years agoHelpfull: Yes(22) No(7)
• Its simple man..
  Digit x must be divisible by 18...i.e. must be divisible by 9 also..
  and only one condition will satisfy that its must all 4s and divided by 9
  i.e. 9 times 4.
  444444444/18= 24691358..minimum no. of digits in 24691358 = 8 digits
• 11 years agoHelpfull: Yes(18) No(2)
• 18x = 444...444
  x = 444...444/18
  x = 222...222/9
  to be able to be divide by 9 (2+2+2+....n times)= 9x
  2n = 9x
  minimun x to achieve such condition = 2
  n = 9
• 11 years agoHelpfull: Yes(4) No(2)
• Hello vinay sipani.. x can not be zero.
  Because if we take x=0 then y will be also 0..
  But it mention thay y should be multiple of 4
• 12 years agoHelpfull: Yes(2) No(4)
• sorry not multiple its all digit as 4s...
• 12 years agoHelpfull: Yes(1) No(4)
• 18x=y
  
  here y is 44.....4
  x can't be zero since y is not zero.
  now,
  
  18x=44....4
  => x=44...4/18
  =>x=22...2/9
  
  to be divisible by 9, sum of digits of that no must be divisible by 9.
  so x=22...2(n times)/9 where n>0
  now for n=1 sum =2 , not divisible by 9
  for n=2 sum=2+2= 4 or 2*2= 4 ,not divisible by 9
  for n=3 sum= 2+2+2=6 or 2*3= 6 ,not divisible by 9
  .
  .
  .
  for n=9 sum= 2*9= 18 ie., divisible by 9
  
  so, x=222222222/9
  x= 24691358
• 7 years agoHelpfull: Yes(1) No(0)
• If its 4s, the digit can be either 4 or 8. So, to make it minimum we need 9 4's or we can take 4 8's and 1 4's as then the sum will be 36 , divisible by 9. So, minimum digits can be 5.
• 11 years agoHelpfull: Yes(0) No(1)