a 4-digit palindrome is a number reading the same front to back and back to front. For example, 1221. We can express a 4-digit palindrome as 1000x + 100y+10y+x= 1001x + 110y. finding a common factor we get. 11(91x+10y) 91 and 10 are coprime or relatively prime. Therefore our answer is 11. Also you could use the divisibility test for 11

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