Something to Think About Day 4 in Number Theory( I think is the way to solve)

a 4digit palindrome is a number reading the same front to back and back to front. For example, 1221. We can express a 4digit 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