Question

Use Euclidean algorithm to find out the Greatest Common Divisor of 36 and 126

Answer 1

The Greatest Common Divisor (GCD) of 36 and 126 is found using the Euclidean algorithm to be 18. This is determined through a series of divisions until the remainder is 0.

Step-by-step explanation:

To find the Greatest Common Divisor (GCD) of 36 and 126 using the Euclidean algorithm, we perform a series of divisions until we obtain a remainder of 0. Here are the steps:

1. Divide the larger number by the smaller number: 126 ÷ 36 = 3 with a remainder of 18.
2. Now divide the previous divisor (36) by the remainder (18): 36 ÷ 18 = 2 with a remainder of 0.
3. Since the remainder is 0, the divisor at this step (18) is the GCD of 36 and 126.

Therefore, the Greatest Common Divisor of 36 and 126 is 18.