Question

Find Greatest Common Divisor of 6437 and 2393, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $6437$ by $2393$ and get the remainder

6437 : 2393 = 2 ( remainder is 1651)

The remainder is positive ( $1651 > 0$ ), so we will continue with division.

Step 2 :
Divide $2393$ by $1651$ and get the remainder

2393 : 1651 = 1 ( remainder is 742)

The remainder is still positive ( $742 > 0$ ), so we will continue with division.

Step 3 :
Divide $1651$ by $742$ and get the remainder

1651 : 742 = 2 ( remainder is 167)

The remainder is still positive ( $167 > 0$ ), so we will continue with division.

Step 4 :
Divide $742$ by $167$ and get the remainder

742 : 167 = 4 ( remainder is 74)

The remainder is still positive ( $74 > 0$ ), so we will continue with division.

Step 5 :
Divide $167$ by $74$ and get the remainder

167 : 74 = 2 ( remainder is 19)

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

Step 6 :
Divide $74$ by $19$ and get the remainder

74 : 19 = 3 ( remainder is 17)

The remainder is still positive ( $17 > 0$ ), so we will continue with division.

Step 7 :
Divide $19$ by $17$ and get the remainder

19 : 17 = 1 ( remainder is 2)

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

Step 8 :
Divide $17$ by $2$ and get the remainder

17 : 2 = 8 ( remainder is 1)

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

Step 9 :
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

6437

2393

157

2393

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

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