Question

Find Greatest Common Divisor of 461 and 722, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $722$ by $461$ and get the remainder

722 : 461 = 1 ( remainder is 261)

The remainder is positive ( $261 > 0$ ), so we will continue with division.

Step 2 :
Divide $461$ by $261$ and get the remainder

461 : 261 = 1 ( remainder is 200)

The remainder is still positive ( $200 > 0$ ), so we will continue with division.

Step 3 :
Divide $261$ by $200$ and get the remainder

261 : 200 = 1 ( remainder is 61)

The remainder is still positive ( $61 > 0$ ), so we will continue with division.

Step 4 :
Divide $200$ by $61$ and get the remainder

200 : 61 = 3 ( remainder is 17)

The remainder is still positive ( $17 > 0$ ), so we will continue with division.

Step 5 :
Divide $61$ by $17$ and get the remainder

61 : 17 = 3 ( remainder is 10)

The remainder is still positive ( $10 > 0$ ), so we will continue with division.

Step 6 :
Divide $17$ by $10$ and get the remainder

17 : 10 = 1 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 7 :
Divide $10$ by $7$ and get the remainder

10 : 7 = 1 ( remainder is 3)

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

Step 8 :
Divide $7$ by $3$ and get the remainder

7 : 3 = 2 ( remainder is 1)

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

Step 9 :
Divide $3$ by $1$ and get the remainder

3 : 1 = 3 ( 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

461

722

461

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

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