Question

Find Greatest Common Divisor of 4711 and 1024, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $4711$ by $1024$ and get the remainder

4711 : 1024 = 4 ( remainder is 615)

The remainder is positive ( $615 > 0$ ), so we will continue with division.

Step 2 :
Divide $1024$ by $615$ and get the remainder

1024 : 615 = 1 ( remainder is 409)

The remainder is still positive ( $409 > 0$ ), so we will continue with division.

Step 3 :
Divide $615$ by $409$ and get the remainder

615 : 409 = 1 ( remainder is 206)

The remainder is still positive ( $206 > 0$ ), so we will continue with division.

Step 4 :
Divide $409$ by $206$ and get the remainder

409 : 206 = 1 ( remainder is 203)

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

Step 5 :
Divide $206$ by $203$ and get the remainder

206 : 203 = 1 ( remainder is 3)

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

Step 6 :
Divide $203$ by $3$ and get the remainder

203 : 3 = 67 ( 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

4711

1024

673

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

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