Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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.