Question

Find Greatest Common Divisor of 1999 and 1090909, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $1090909$ by $1999$ and get the remainder

1090909 : 1999 = 545 ( remainder is 1454)

The remainder is positive ( $1454 > 0$ ), so we will continue with division.

Step 2 :
Divide $1999$ by $1454$ and get the remainder

1999 : 1454 = 1 ( remainder is 545)

The remainder is still positive ( $545 > 0$ ), so we will continue with division.

Step 3 :
Divide $1454$ by $545$ and get the remainder

1454 : 545 = 2 ( remainder is 364)

The remainder is still positive ( $364 > 0$ ), so we will continue with division.

Step 4 :
Divide $545$ by $364$ and get the remainder

545 : 364 = 1 ( remainder is 181)

The remainder is still positive ( $181 > 0$ ), so we will continue with division.

Step 5 :
Divide $364$ by $181$ and get the remainder

364 : 181 = 2 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 6 :
Divide $181$ by $2$ and get the remainder

181 : 2 = 90 ( remainder is 1)

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

Step 7 :
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

1999

1090909

1999

1090909

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

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