Question

Using Euclidean algorithm find the greatest common divisor of 66 and 42

Answer 1

Using the Euclidean algorithm, the greatest common divisor of 66 and 42 is found to be 6, determined through a series of divisions until a remainder of 0 is reached.

Step-by-step explanation:

To find the greatest common divisor (GCD) of 66 and 42 using the Euclidean algorithm, we repeatedly apply the basic step of the algorithm until we get a remainder of 0. Here is how it works:

1. Divide 66 by 42 to get a quotient and a remainder. 66 = 42 × 1 + 24.
2. Now take the previous divisor (42) and divide it by the remainder (24) from the first step. 42 = 24 × 1 + 18.
3. Continue the process: divide 24 (previous remainder) by 18 (new remainder). 24 = 18 × 1 + 6.
4. Now, divide 18 by the last remainder 6. 18 = 6 × 3 + 0. When we reach a remainder of 0, we stop the algorithm. The last non-zero remainder is the GCD. In this case, the GCD is 6.

Therefore, the greatest common divisor of 66 and 42 is 6.