Question

Find Greatest Common Divisor of 1492 and 1066, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $1492$ by $1066$ and get the remainder

1492 : 1066 = 1 ( remainder is 426)

The remainder is positive ( $426 > 0$ ), so we will continue with division.

Step 2 :
Divide $1066$ by $426$ and get the remainder

1066 : 426 = 2 ( remainder is 214)

The remainder is still positive ( $214 > 0$ ), so we will continue with division.

Step 3 :
Divide $426$ by $214$ and get the remainder

426 : 214 = 1 ( remainder is 212)

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

Step 4 :
Divide $214$ by $212$ and get the remainder

214 : 212 = 1 ( remainder is 2)

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

Step 5 :
Divide $212$ by $2$ and get the remainder

212 : 2 = 106 ( remainder is 0)

The remainder is zero => GCD is the last divisor $2$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1492

1066

373

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

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