Question

Find Greatest Common Divisor of 129 and 236, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $236$ by $129$ and get the remainder

236 : 129 = 1 ( remainder is 107)

The remainder is positive ( $107 > 0$ ), so we will continue with division.

Step 2 :
Divide $129$ by $107$ and get the remainder

129 : 107 = 1 ( remainder is 22)

The remainder is still positive ( $22 > 0$ ), so we will continue with division.

Step 3 :
Divide $107$ by $22$ and get the remainder

107 : 22 = 4 ( remainder is 19)

The remainder is still positive ( $19 > 0$ ), so we will continue with division.

Step 4 :
Divide $22$ by $19$ and get the remainder

22 : 19 = 1 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 5 :
Divide $19$ by $3$ and get the remainder

19 : 3 = 6 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 6 :
Divide $3$ by $1$ and get the remainder

3 : 1 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

129

236

The GCD equals the product of the numbers at the intersection.

This page was created using

GCD Calculator