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Numerous tasks in Computer Science lead to computation of greatest common divisor. In this book the focus is on optimization of known realizations based on Knuth's ideas. We make attempts to minimize the number of assignments and the number of comparisons. These algorithms are commented and cited in every book of algorithms. The new insight in novel algorithms' realization presented in this book is that we unite the two iteration steps into one with aim to receive solutions for shorter CPU time and our approach become in the style of Anatoly Karatsuba's "divide and conquer" algorithmic technique. We receive some benefits and our results can be reflect in many books for classical algebra in present days. The ideas in presented algorithms here can be used in training for hard programming contents such as International Olympiad in Informatics (IOI). The book will be extremely useful for students, teachers in algorithms, PhD students, university lecturers in algebra, professionals and specialists in Computer Science, Algorithm Complexity', Speed of Computer Programmes Performance and for every who deals with practical solutions using programming languages and contemporary computers.