Question

Find Greatest Common Divisor of 6897 and 9481, using Euclidean algorithm.

Answer

The GCD of given numbers is 19.

Explanation

Step 1 :
Divide $9481$ by $6897$ and get the remainder

9481 : 6897 = 1 ( remainder is 2584)

The remainder is positive ( $2584 > 0$ ), so we will continue with division.

Step 2 :
Divide $6897$ by $2584$ and get the remainder

6897 : 2584 = 2 ( remainder is 1729)

The remainder is still positive ( $1729 > 0$ ), so we will continue with division.

Step 3 :
Divide $2584$ by $1729$ and get the remainder

2584 : 1729 = 1 ( remainder is 855)

The remainder is still positive ( $855 > 0$ ), so we will continue with division.

Step 4 :
Divide $1729$ by $855$ and get the remainder

1729 : 855 = 2 ( remainder is 19)

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

Step 5 :
Divide $855$ by $19$ and get the remainder

855 : 19 = 45 ( remainder is 0)

The remainder is zero => GCD is the last divisor $19$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

6897

9481

499

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

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