A Concrete Introduction to Higher Algebra pp 27-52 | Cite as

# Euclid's Algorithm

Chapter

This chapter begins with the Division Theorem, a result that describes the result of long division of numbers. Repeated use of the Division Theorem yields the description of any number in base *a* (e.g. *a* = 2, or *a* = 16 or *a* = 60). Repeated use also yields Euclid's Algorithm for finding the greatest common divisor of two numbers. Euclid's Algorithm dates from the 4th century B. C., but remains one of the fastest and most useful algorithms in modern computational number theory, and has important theoretical consequences for the set ℤ of integers.

## Keywords

Natural Number Great Common Divisor Fibonacci Number Golden Ratio Decimal Digit
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2009