Question

Find Greatest Common Divisor of 2349 and 1537, using Euclidean algorithm.

Answer

The GCD of given numbers is 29.

Explanation

Step 1 :
Divide $2349$ by $1537$ and get the remainder

2349 : 1537 = 1 ( remainder is 812)

The remainder is positive ( $812 > 0$ ), so we will continue with division.

Step 2 :
Divide $1537$ by $812$ and get the remainder

1537 : 812 = 1 ( remainder is 725)

The remainder is still positive ( $725 > 0$ ), so we will continue with division.

Step 3 :
Divide $812$ by $725$ and get the remainder

812 : 725 = 1 ( remainder is 87)

The remainder is still positive ( $87 > 0$ ), so we will continue with division.

Step 4 :
Divide $725$ by $87$ and get the remainder

725 : 87 = 8 ( remainder is 29)

The remainder is still positive ( $29 > 0$ ), so we will continue with division.

Step 5 :
Divide $87$ by $29$ and get the remainder

87 : 29 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $29$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

2349

1537

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

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