How many 6 digit palindromes are divisible by 8?

• answer is 100
  
  
  Let the 6 digit palindromic number is abccba
  a≠0 , Because then the number will become a five digit number
  
  Now let's come to the point of divisibility by 8.
  
  When the last three digit of a number is evenly divisible by 8 then the whole number is divisible by 8.
  
  So here if 8 divides cba then it will also divide abccba.
  
  cba can be any number from 001 to 999 if a≠0.
  
  So cba can't be a number which ends with 0 .
  
  Now for knowing how many numbers from 1 to 999 is divisible by 8 we will divide 999 by 8 and take the quotient.We get 124 as quotient by dividing 999 by 8.
  
  But as the 6 digit palindromic numbers can't end with a zero we can't take the numbers which ends with a zero.
  
  The numbers which end with a zero can be divided by 5. Again a number which can be divided by both 5 and 8 can also be divided by 40.
  
  From 1 to 999 there are 24 numbers which can be divided by 40.(by dividing 999 by 40 and taking the quotient.)
  
  So there are 124−24
  
  100 six digit palindromic numbers which can be divided by 8.
• 10 years agoHelpfull: Yes(41) No(3)
• The no.of palindromes are:100
  Because the 6 digit palindromes are divisible by 8.
  It means that the last 3 digits are divisible by 8.
  B/w 0 and 999 the no.of digits which are divisible by 8 are 124.
  and the last digit should not end with 0 since it will become a 5 digit no in palindrome.
  The digits which are divisible by 8 and end with 0 are 24.
  Hence the total palindromes which are obtained are 124-24=100.
• 10 years agoHelpfull: Yes(5) No(0)
• Divisibility rule of 8- last 3 digit no must be divisible by 8.
  First 6 digit no which is divisible by 8 is 800(008) as 008 is divisible by 8.
  
  Then
  
  800(008) [8x1=8]
  610(016) [8x2=16]
  240(024) [8x3=24]
  ....
  299(992) [8x124=992]
  
  total no will be 124
  
  6 digit palindrome no should not end with a 0.
  so we have
  
  8x5=40 [6 digit no should not be like 040040]
  8x10=80 [6 digit no should not be like 080080]
  8x15=120 [6 digit no should not be like 012120]
  ....
  
  let n be the no of possible such no ends with a 0
  
  Then 5+(n-1)5=120
  n=24
  
  Ans: 124-24=100
• 10 years agoHelpfull: Yes(1) No(0)
• diMag ki band bja di.
• 10 years agoHelpfull: Yes(1) No(1)
• diMag ki band bja di.
• 10 years agoHelpfull: Yes(0) No(0)