Prime Station: The Factor Code
Orbital Station Kepler-9 is crippled and adrift. Every critical system is sealed behind factor-encrypted bulkheads. As the cadet on duty, only your command of prime factorization and the greatest common factor can bring the station back online — before life support fails.
The Locked Bay
The Twin Engines
The Master Door
Station Restored — Mission Complete!
Kepler-9 is fully online. You decomposed every lock into its prime factors, synced the engines with the GCF, and cracked the reactor’s combined cipher. Command has logged a commendation, Captain.
Prove your rank to certify your Master Certificate!
The final mainframe seal requires the GCF of 108 and 144. Given $108 = 2^2 \times 3^3$ and $144 = 2^4 \times 3^2$, extract the lowest power of each shared prime to solve.