### Instruction: What is the greatest common factor of all two-digit palindromes?  (Note: A palindrome is a number that reads the same forwards as backwards.).### Response: I know that the two-digit palindromes are 11, 22, 33, 44, 55, 66, 77, 88, and 99.
To find the greatest common factor of these numbers, I can look at their prime factorizations.
11 is already prime, so I can't factor it further.
22 is 2 times 11, 33 is 3 times 11, 44 is 2 times 2 times 11, and so on.
I notice that every two-digit palindrome has a factor of 11, and some have other factors as well.
Therefore, the greatest common factor of all two-digit palindromes must be 11, since it is the largest factor that they all share.