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(Euclidean Algorithm) As mentioned in class, the Euclidean algorithm is useful for finding the GCD of two numbers A and B by producing the sequence $R_n$ by $R_1$ = mod (A, B), $R_2$ = mod (B, $R_1$), $R_n$ = mod ($R_{n-2}$, $R_{n-1}$) for n ? 2. The last non-zero number in the sequence is the GCD of A and B. euclid_gcd Function: Input variables: • a scalar representing A • a scalar representing B (which you may assume is not equal to A) Output variables: • a scalar representing the GCD of A and B • a vector of all iterates produced (this vector should include $R_1$ and $R_2$ as its first entries as well as the final zero entry) A possible sample case is: >> [GCD, R] = euclid_gcd(32, 40) GCD = 8 R = 32 8 0 >> [GCD, R] = euclid_gcd(100, 65) GCD = 5 R = 35 30 5 0

          (Euclidean Algorithm) As mentioned in class, the Euclidean algorithm is useful for
finding the GCD of two numbers A and B by producing the sequence $R_n$ by
$R_1$ = mod (A, B), $R_2$ = mod (B, $R_1$), $R_n$ = mod ($R_{n-2}$, $R_{n-1}$)
for n ? 2. The last non-zero number in the sequence is the GCD of A and B.
euclid_gcd Function:
Input variables:
• a scalar representing A
• a scalar representing B (which you may assume is not equal to A)
Output variables:
• a scalar representing the GCD of A and B
• a vector of all iterates produced (this vector should include $R_1$ and $R_2$ as
its first entries as well as the final zero entry)
A possible sample case is:
>> [GCD, R] = euclid_gcd(32, 40)
GCD = 8
R =
32 8 0
>> [GCD, R] = euclid_gcd(100, 65)
GCD = 5
R =
35 30 5 0

(Euclidean Algorithm) As mentioned in class, the Euclidean algorithm is useful for
finding the GCD of two numbers A and B by producing the sequence Rn by
R1 = mod (A, B), R2 = mod (B, R1), Rn = mod (Rn-2, Rn-1)
for n ? 2. The last non-zero number in the sequence is the GCD of A and B.
euclidgcd Function:
Input variables:
• a scalar representing A
• a scalar representing B (which you may assume is not equal to A)
Output variables:
• a scalar representing the GCD of A and B
• a vector of all iterates produced (this vector should include R1 and R2 as
its first entries as well as the final zero entry)
A possible sample case is:
>> [GCD, R] = euclidgcd(32, 40)
GCD = 8
R =
32 8 0
>> [GCD, R] = euclidgcd(100, 65)
GCD = 5
R =
35 30 5 0

Added by Carla A.

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