Consider how the Euclidean algorithm reduces the problem size using modulo operations, and how bitwise operations might optimize these reductions.

Explore the binary GCD algorithm (Stein's algorithm), which replaces modulo operations with bit shifts and subtractions, and analyze its efficiency compared to the standard Euclidean algorithm.

Investigate the role of bitwise AND operations in determining the greatest power of 2 dividing both numbers, and how this can be used to further optimize the GCD computation.