Question

Find Greatest Common Divisor of 2689 and 1369, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $2689$ by $1369$ and get the remainder

2689 : 1369 = 1 ( remainder is 1320)

The remainder is positive ( $1320 > 0$ ), so we will continue with division.

Step 2 :
Divide $1369$ by $1320$ and get the remainder

1369 : 1320 = 1 ( remainder is 49)

The remainder is still positive ( $49 > 0$ ), so we will continue with division.

Step 3 :
Divide $1320$ by $49$ and get the remainder

1320 : 49 = 26 ( remainder is 46)

The remainder is still positive ( $46 > 0$ ), so we will continue with division.

Step 4 :
Divide $49$ by $46$ and get the remainder

49 : 46 = 1 ( remainder is 3)

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

Step 5 :
Divide $46$ by $3$ and get the remainder

46 : 3 = 15 ( 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

2689

1369

2689

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

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