How does the Euclidean algorithm find the greatest common divisor of 544 and 119?

To find the greatest common divisor (GCD) of 544 and 119 using the Euclidean algorithm, you perform a series of divisions to find successive remainders until the remainder is zero. The last non-zero remainder is the GCD.12

The process for 544 and 119 is as follows:

• 544 = 4 × 119 + 68
• 119 = 1 × 68 + 51
• 68 = 1 × 51 + 17
• 51 = 3 × 17 + 0

Because the final remainder is 0, the process concludes. The last non-zero remainder is 17, which is the greatest common divisor of 544 and 119.2