Question

Find Greatest Common Divisor of 1819 and 3587, using Euclidean algorithm.

Answer

The GCD of given numbers is 17.

Explanation

Step 1 :
Divide $3587$ by $1819$ and get the remainder

3587 : 1819 = 1 ( remainder is 1768)

The remainder is positive ( $1768 > 0$ ), so we will continue with division.

Step 2 :
Divide $1819$ by $1768$ and get the remainder

1819 : 1768 = 1 ( remainder is 51)

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

Step 3 :
Divide $1768$ by $51$ and get the remainder

1768 : 51 = 34 ( remainder is 34)

The remainder is still positive ( $34 > 0$ ), so we will continue with division.

Step 4 :
Divide $51$ by $34$ and get the remainder

51 : 34 = 1 ( remainder is 17)

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

Step 5 :
Divide $34$ by $17$ and get the remainder

34 : 17 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $17$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1819

3587

107

211

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

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