tl;dr:1. Notice repeating pattern in AES-ECB encrypted private key2. Notice that one of the primes has to be in a form `k * 0x1000...10000...100001 +S`3. Use Coppersmith method to find small roots of polynomial `f(x) = N/pattern -x`4. Recover prime factors
Full writeup: https://github.com/p4-team/ctf/tree/master/2019-11-02-google-ctf/fractorization