Question

Find Greatest Common Divisor of 1586 and 899, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $1586$ by $899$ and get the remainder

1586 : 899 = 1 ( remainder is 687)

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

Step 2 :
Divide $899$ by $687$ and get the remainder

899 : 687 = 1 ( remainder is 212)

The remainder is still positive ( $212 > 0$ ), so we will continue with division.

Step 3 :
Divide $687$ by $212$ and get the remainder

687 : 212 = 3 ( remainder is 51)

The remainder is still positive ( $51 > 0$ ), so we will continue with division.

Step 4 :
Divide $212$ by $51$ and get the remainder

212 : 51 = 4 ( remainder is 8)

The remainder is still positive ( $8 > 0$ ), so we will continue with division.

Step 5 :
Divide $51$ by $8$ and get the remainder

51 : 8 = 6 ( remainder is 3)

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

Step 6 :
Divide $8$ by $3$ and get the remainder

8 : 3 = 2 ( 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

1586

899

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

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