Question

Find Greatest Common Divisor of 294 and 654, using Euclidean algorithm.

Answer

The GCD of given numbers is 6.

Explanation

Step 1 :
Divide $654$ by $294$ and get the remainder

654 : 294 = 2 ( remainder is 66)

The remainder is positive ( $66 > 0$ ), so we will continue with division.

Step 2 :
Divide $294$ by $66$ and get the remainder

294 : 66 = 4 ( remainder is 30)

The remainder is still positive ( $30 > 0$ ), so we will continue with division.

Step 3 :
Divide $66$ by $30$ and get the remainder

66 : 30 = 2 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 4 :
Divide $30$ by $6$ and get the remainder

30 : 6 = 5 ( remainder is 0)

The remainder is zero => GCD is the last divisor $6$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

294

654

109

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

This page was created using

GCD Calculator