2023 AMC 10A Problem 23

Positive integer divisors a and b of N are called complementary if ab = N. Given that N has a pair of complementary divisors that differ by 20 and a pair of complementary divisors that differ by 23, find the sum of the digits of N.

\textbf{(A)} 11 \qquad \textbf{(B)} 13 \qquad \textbf{(C)} 15 \qquad \textbf{(D)} 17 \qquad \textbf{(E)} 19

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.