Six of the factors of 1221 are palindromes: {1,3,11,33,111,1221} but two are not: {37,407}

(A) What number under one million has the most palindrome factors?

Some numbers have only palindromes as factors. Examples include 88: {1,2,4,8,11,22,44,88} and any palindromic prime

(B) Find the smallest number with at least as many palindrome factors as part (A) but having only palindrome factors.