Question

Find Greatest Common Divisor of 12327 and 2409, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $12327$ by $2409$ and get the remainder

12327 : 2409 = 5 ( remainder is 282)

The remainder is positive ( $282 > 0$ ), so we will continue with division.

Step 2 :
Divide $2409$ by $282$ and get the remainder

2409 : 282 = 8 ( remainder is 153)

The remainder is still positive ( $153 > 0$ ), so we will continue with division.

Step 3 :
Divide $282$ by $153$ and get the remainder

282 : 153 = 1 ( remainder is 129)

The remainder is still positive ( $129 > 0$ ), so we will continue with division.

Step 4 :
Divide $153$ by $129$ and get the remainder

153 : 129 = 1 ( remainder is 24)

The remainder is still positive ( $24 > 0$ ), so we will continue with division.

Step 5 :
Divide $129$ by $24$ and get the remainder

129 : 24 = 5 ( remainder is 9)

The remainder is still positive ( $9 > 0$ ), so we will continue with division.

Step 6 :
Divide $24$ by $9$ and get the remainder

24 : 9 = 2 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 7 :
Divide $9$ by $6$ and get the remainder

9 : 6 = 1 ( remainder is 3)

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

Step 8 :
Divide $6$ by $3$ and get the remainder

6 : 3 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

12327

2409

587

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

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