1. Which of the following statements help to explain how the Euclidean algorithm
ID: 3146625 • Letter: 1
Question
1. Which of the following statements help to explain how the Euclidean algorithm works? (Select all that apply.)
a. We can find GCDs using prime factorizations.
b. gcd(b,0)=b for any integer b>0.
c. At each stage we reduce the problem to a smaller instance.
d. All prime numbers except 2 are odd.
e. If r = a mod b then gcd(a,b) = gcd(b,r).
a. We can find GCDs using prime factorizations.
b. gcd(b,0)=b for any integer b>0.
c. At each stage we reduce the problem to a smaller instance.
d. All prime numbers except 2 are odd.
e. If r = a mod b then gcd(a,b) = gcd(b,r).
Explanation / Answer
The Euclidean algorithm uses the following steps in order:
e. If r = a mod b then gcd(a,b) = gcd(b,r).
c. At each stage we reduce the problem to a smaller instance.
b. gcd(b,0)=b for any integer b>0.
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