Question

Find Greatest Common Divisor of 69 and 19, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $69$ by $19$ and get the remainder

69 : 19 = 3 ( remainder is 12)

The remainder is positive ( $12 > 0$ ), so we will continue with division.

Step 2 :
Divide $19$ by $12$ and get the remainder

19 : 12 = 1 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 3 :
Divide $12$ by $7$ and get the remainder

12 : 7 = 1 ( remainder is 5)

The remainder is still positive ( $5 > 0$ ), so we will continue with division.

Step 4 :
Divide $7$ by $5$ and get the remainder

7 : 5 = 1 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 5 :
Divide $5$ by $2$ and get the remainder

5 : 2 = 2 ( remainder is 1)

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

Step 6 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( 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

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

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