Elliptic Curve Cryptography (ECC) does not rely on the prime factorization problem. Instead, ECC is based on the mathematical difficulty of solving elliptic curve discrete logarithm problems.
RSA relies directly on the difficulty of factoring large prime numbers. GPG and PGP are encryption tools and standards that may use RSA or other algorithms internally.
ECC provides equivalent security with much smaller key sizes, making it efficient for mobile devices, embedded systems, and environments with limited processing power.
Modern security standards increasingly recommend ECC due to its performance and strong security properties.