13. We will call a two-digit number power-less if neither of its digits can be written as an integer to a power greater than 1. For example, 53 is power-less, but 54 is not power-less since $4=2^{2}$. Which of the following is a common divisor of the smallest and the largest power-less numbers?
A 3
B 5
C 7
D 11
E 13
SOLUTION
D

The digits of a power-less number can be only $2,3,5,6$, and 7 . The smallest two-digit number is 22 and the largest one is 77 , and they have a common divisor of 11 .