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Chapter 4 Greatest Common Divisors
Objectives
Determine whether an integer divides another integer.
Recognize the Euclidean algorithm.
Compute greatest common divisors.
Compute the cofactors from a special case of Bézout’s identity.
Next, we introduce the Euclidean Algorithm (
Algorithm 4.3.2 ). This algorithm gives step-by-step instructions for finding the greatest common divisor of two natural numbers. Then, we use the computations in the Euclidean Algorithm (
Algorithm 4.3.2 ) to find the integers whose existence is guaranteed by Bézout’s identity (
Theorem 4.4.1 ).
