Use the Euclidean algorithm to calculate gcd832 144 Show eac

Use the Euclidean algorithm to calculate gcd(832, 144). Show each step in the reduction until you get to the final end step as shown in the notes. Do not stop when you can guess the answer.

Solution

Euclidean algorithm:

Step 1: 832 = 5*144 + 112

Step 2: 144 = 1*112 + 32

Step 3: 112 = 3*32 + 16

Step 4: 32 = 2*16

Therefore: gcd(832, 144) = 16.