Is a palindrome number divisible by 11?

What is a palindrome number?

• A palindrome is something that reads from left to right and from right to left has the same meaning and the same sequence of characters.
• Thus, a palindrome number is a number that meets the definition of a palindrome. There are not only the best-known two-digit palindromic numbers, but an infinite number.
• There are 9 two-digit palindromic numbers, of which 11 is the smallest palindromic number. The other two-digit Counting are: 22, 33, 44, 55, 66, 77, 88 and 99. In general, these special two-digit numbers can be represented by XX or by the term 11 * x.
• The palindromes include not only two-digit, but also three-digit, four-digit, five-digit, etc. Counting. Three-digit numbers generally have the form XYX or can be expressed using the term 101 * x + 10 * y. Here x and y can have different values. A few examples of three-digit palindromes are: 111, 121, 131, 515, 949, and 909.
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• With four-digit palindromic numbers, the form XYYX is adhered to, so that these numbers can also be represented by 1001 * x + 110 * y. Five-digit palindromes can be represented by three variables, resulting in: XYZYX or 10001 * x + 1010 * y + 100 * z. For even larger numbers, the principle for palindromes is continued in the same way.


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Are palindromes divisible by 11?

• 11 is the smallest palindrome number. This naturally suggests that all palindromic numbers could be divisible by 11. Since the two-digit palindromic numbers are all multiples of 11, the assumption for these numbers is definitely correct.
• However, as soon as a palindrome has three digits or even larger, it can be divisible by 11, but does not have to be. All palindromes that are a multiple of 11 * 11, i.e. 121, can also be divided by 11. This applies to the numbers 121, 242, 363 and 484.
• For the remaining and higher palindromic numbers, you should use the normal arithmetic rules to check whether this number is completely divisible by 11. This is the case when the alternating checksum resp. the 2's cross-sum of a number is evenly divisible by 11.