Question

Find Greatest Common Divisor of 36243 and 4866, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $36243$ by $4866$ and get the remainder

36243 : 4866 = 7 ( remainder is 2181)

The remainder is positive ( $2181 > 0$ ), so we will continue with division.

Step 2 :
Divide $4866$ by $2181$ and get the remainder

4866 : 2181 = 2 ( remainder is 504)

The remainder is still positive ( $504 > 0$ ), so we will continue with division.

Step 3 :
Divide $2181$ by $504$ and get the remainder

2181 : 504 = 4 ( remainder is 165)

The remainder is still positive ( $165 > 0$ ), so we will continue with division.

Step 4 :
Divide $504$ by $165$ and get the remainder

504 : 165 = 3 ( remainder is 9)

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

Step 5 :
Divide $165$ by $9$ and get the remainder

165 : 9 = 18 ( remainder is 3)

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

Step 6 :
Divide $9$ by $3$ and get the remainder

9 : 3 = 3 ( 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

36243

4866

4027

811

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

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