Question

Find Greatest Common Divisor of 259 and 621, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $621$ by $259$ and get the remainder

621 : 259 = 2 ( remainder is 103)

The remainder is positive ( $103 > 0$ ), so we will continue with division.

Step 2 :
Divide $259$ by $103$ and get the remainder

259 : 103 = 2 ( remainder is 53)

The remainder is still positive ( $53 > 0$ ), so we will continue with division.

Step 3 :
Divide $103$ by $53$ and get the remainder

103 : 53 = 1 ( remainder is 50)

The remainder is still positive ( $50 > 0$ ), so we will continue with division.

Step 4 :
Divide $53$ by $50$ and get the remainder

53 : 50 = 1 ( remainder is 3)

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

Step 5 :
Divide $50$ by $3$ and get the remainder

50 : 3 = 16 ( remainder is 2)

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

Step 6 :
Divide $3$ by $2$ and get the remainder

3 : 2 = 1 ( remainder is 1)

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

Step 7 :
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

259

621

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

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