Question

Suppose you were trying to find the greatest common divisor of 7,398 and 2,877 using the Euclidean Algorithm. Recall that for step 1, 7398= "big" and 2877= "small." After applying Step 1 of the algorithm, the number the number is the new "big" and is the new "small." There may be more than one right answer! Hint: If you watched the videos, this problem is super easy!

A.2877,1644
B.2877,2
C.small,
D.big % small

Answer 1

To find the GCD of 7,398 and 2,877 using the Euclidean Algorithm, after the first division, 2,877 is the new 'big' and 1,644 is the new 'small'. The process is repeated until the remainder is 0, at which point the 'big' is the GCD.

Step-by-step explanation:

The greatest common divisor (GCD) of 7,398 and 2,877 can be found using the Euclidean Algorithm. In the first step of the algorithm, we divide the larger number (7,398) by the smaller number (2,877). The remainder becomes the new 'small' number in the next iteration, while the 'small' from the previous iteration becomes the new 'big' number. This process is repeated until the remainder is 0.

Applying the first step, we get:

7398 = 2877 × 2 + 1644

In this case, 2877 remains as the 'big' and 1644 is the new 'small'. We will continue this process until the 'small' becomes 0, at which point the 'big' will be the GCD.

Following this method, the number 2,877 becomes the new "big" and 1,644 becomes the new "small" after the first step.