Question

Find Greatest Common Divisor of 6897 and 1597, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $6897$ by $1597$ and get the remainder

6897 : 1597 = 4 ( remainder is 509)

The remainder is positive ( $509 > 0$ ), so we will continue with division.

Step 2 :
Divide $1597$ by $509$ and get the remainder

1597 : 509 = 3 ( remainder is 70)

The remainder is still positive ( $70 > 0$ ), so we will continue with division.

Step 3 :
Divide $509$ by $70$ and get the remainder

509 : 70 = 7 ( remainder is 19)

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

Step 4 :
Divide $70$ by $19$ and get the remainder

70 : 19 = 3 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 5 :
Divide $19$ by $13$ and get the remainder

19 : 13 = 1 ( remainder is 6)

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

Step 6 :
Divide $13$ by $6$ and get the remainder

13 : 6 = 2 ( remainder is 1)

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

Step 7 :
Divide $6$ by $1$ and get the remainder

6 : 1 = 6 ( 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

6897

1597

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

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