Question 81
Consider the number $N=1000\ldots 0001$ consisting of the digit one followed by 2023 zeros, followed in turn by the digit one. How many proper divisors of $N$ (that is, divisors strictly between 1 and $N$) are also written as a digit 1 followed by some positive number of zeros, followed in turn by a digit 1?
(A) 3
(B) 5
(C) 12
(D) 14
(E) 16
(A) 3
(B) 5
(C) 12
(D) 14
(E) 16