Question

Find Greatest Common Divisor of 2533 and 466, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $2533$ by $466$ and get the remainder

2533 : 466 = 5 ( remainder is 203)

The remainder is positive ( $203 > 0$ ), so we will continue with division.

Step 2 :
Divide $466$ by $203$ and get the remainder

466 : 203 = 2 ( remainder is 60)

The remainder is still positive ( $60 > 0$ ), so we will continue with division.

Step 3 :
Divide $203$ by $60$ and get the remainder

203 : 60 = 3 ( remainder is 23)

The remainder is still positive ( $23 > 0$ ), so we will continue with division.

Step 4 :
Divide $60$ by $23$ and get the remainder

60 : 23 = 2 ( remainder is 14)

The remainder is still positive ( $14 > 0$ ), so we will continue with division.

Step 5 :
Divide $23$ by $14$ and get the remainder

23 : 14 = 1 ( remainder is 9)

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

Step 6 :
Divide $14$ by $9$ and get the remainder

14 : 9 = 1 ( remainder is 5)

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

Step 7 :
Divide $9$ by $5$ and get the remainder

9 : 5 = 1 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 8 :
Divide $5$ by $4$ and get the remainder

5 : 4 = 1 ( remainder is 1)

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

Step 9 :
Divide $4$ by $1$ and get the remainder

4 : 1 = 4 ( 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

2533

466

149

233

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

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