Question

Find Greatest Common Divisor of 345 and 587, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $587$ by $345$ and get the remainder

587 : 345 = 1 ( remainder is 242)

The remainder is positive ( $242 > 0$ ), so we will continue with division.

Step 2 :
Divide $345$ by $242$ and get the remainder

345 : 242 = 1 ( remainder is 103)

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

Step 3 :
Divide $242$ by $103$ and get the remainder

242 : 103 = 2 ( remainder is 36)

The remainder is still positive ( $36 > 0$ ), so we will continue with division.

Step 4 :
Divide $103$ by $36$ and get the remainder

103 : 36 = 2 ( remainder is 31)

The remainder is still positive ( $31 > 0$ ), so we will continue with division.

Step 5 :
Divide $36$ by $31$ and get the remainder

36 : 31 = 1 ( remainder is 5)

The remainder is still positive ( $5 > 0$ ), so we will continue with division.

Step 6 :
Divide $31$ by $5$ and get the remainder

31 : 5 = 6 ( remainder is 1)

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

Step 7 :
Divide $5$ by $1$ and get the remainder

5 : 1 = 5 ( 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

345

587

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

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