Question

Find Greatest Common Divisor of 3187024 and 5723, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $3187024$ by $5723$ and get the remainder

3187024 : 5723 = 556 ( remainder is 5036)

The remainder is positive ( $5036 > 0$ ), so we will continue with division.

Step 2 :
Divide $5723$ by $5036$ and get the remainder

5723 : 5036 = 1 ( remainder is 687)

The remainder is still positive ( $687 > 0$ ), so we will continue with division.

Step 3 :
Divide $5036$ by $687$ and get the remainder

5036 : 687 = 7 ( remainder is 227)

The remainder is still positive ( $227 > 0$ ), so we will continue with division.

Step 4 :
Divide $687$ by $227$ and get the remainder

687 : 227 = 3 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 5 :
Divide $227$ by $6$ and get the remainder

227 : 6 = 37 ( remainder is 5)

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

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

6 : 5 = 1 ( remainder is 1)

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

Step 7 :
Divide $5$ by $1$ and get the remainder

5 : 1 = 5 ( 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

3187024

5723

11717

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

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