Abstract
In Section 2.8, the definition of the greatest common divisor of two (or more) integers was introduced, and this concept was used in Chap. 3 in order to determine whether or not a particular right triangle was primitive. In Exercise 34 of Section 3.2, you were asked to determine whether or not 100 − 621 − 629 was a primitive Pythagorean triple. Larger numbers made it more difficult to find the greatest common divisor by trial and error, but this problem came up again as Example 4.9, where prime factorizations were used to make it easier to find the greatest common divisor of these three numbers. In this Chapter, we introduce another method for finding greatest common divisors called the Euclidean Algorithm.
“An algorithm must be seen to be believed.”
—Donald Knuth, 1938–Present
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- 1.
The “division algorithm” is technically not an algorithm under this definition, but this name has become standard.
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© 2015 Sylvia Forman and Agnes M. Rash
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Forman, S., Rash, A.M. (2015). The Euclidean Algorithm. In: The Whole Truth About Whole Numbers. Springer, Cham. https://doi.org/10.1007/978-3-319-11035-6_5
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DOI: https://doi.org/10.1007/978-3-319-11035-6_5
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