Find the 6 digit palindrome divisible by 55.

1.	Find the 6 digit palindrome divisible by 55.
Answer» The number is divisible by 55. So, it must be divide by 5 & 11. ∴ last digit must be 0, 5 But in a palindrome number last digit is equal to first digit & first digit never be zero. ∴ last digit never be 0. ∴ only possibility for last digit is 5. Number is palindrome ∴ 2nd & 5th digits are same Also 3rd & 4th digits are same. Number is divisible by 11. So, difference of (first digit + 3rd digit + 5th digit) & (2nd digit + 4th digit + 6th digit) is zero or multiple of 11. So, a palindrome number of even digits are always divisible by 11. The palindrome number which is divisible by 55 are 5abba5, a, b ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

Answer»

The number is divisible by 55.

So, it must be divide by 5 & 11.

∴ last digit must be 0, 5

But in a palindrome number last digit is equal to first digit & first digit never be zero.

∴ last digit never be 0.

∴ only possibility for last digit is 5.

Number is palindrome

∴ 2nd & 5th digits are same

Also 3rd & 4th digits are same.

Number is divisible by 11.

So, difference of (first digit + 3rd digit + 5th digit) & (2nd digit + 4th digit + 6th digit) is zero or multiple of 11.

So, a palindrome number of even digits are always divisible by 11.

The palindrome number which is divisible by 55 are 5abba5, a, b ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

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