 In essence, one extracts initial digits, typically forming one or two computer words, and runs Euclid's algorithms on these smaller numbers, as long as it is guaranteed that the quotients are the same with those that would be obtained with the original numbers.Those quotients are collected into a small 2-by-2 transformation matrix (that is a matrix of single-word integers), for using them all at once for reducing the original numbers.This process is repeated until numbers have a size for which the binary algorithm (see below) is more efficient.