Question

Find Greatest Common Divisor of 466 and 267, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $466$ by $267$ and get the remainder

466 : 267 = 1 ( remainder is 199)

The remainder is positive ( $199 > 0$ ), so we will continue with division.

Step 2 :
Divide $267$ by $199$ and get the remainder

267 : 199 = 1 ( remainder is 68)

The remainder is still positive ( $68 > 0$ ), so we will continue with division.

Step 3 :
Divide $199$ by $68$ and get the remainder

199 : 68 = 2 ( remainder is 63)

The remainder is still positive ( $63 > 0$ ), so we will continue with division.

Step 4 :
Divide $68$ by $63$ and get the remainder

68 : 63 = 1 ( remainder is 5)

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

Step 5 :
Divide $63$ by $5$ and get the remainder

63 : 5 = 12 ( remainder is 3)

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

Step 6 :
Divide $5$ by $3$ and get the remainder

5 : 3 = 1 ( remainder is 2)

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

Step 7 :
Divide $3$ by $2$ and get the remainder

3 : 2 = 1 ( remainder is 1)

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

Step 8 :
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

466

267

233

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

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