Question

Find Greatest Common Divisor of 765844 and 8362, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $765844$ by $8362$ and get the remainder

765844 : 8362 = 91 ( remainder is 4902)

The remainder is positive ( $4902 > 0$ ), so we will continue with division.

Step 2 :
Divide $8362$ by $4902$ and get the remainder

8362 : 4902 = 1 ( remainder is 3460)

The remainder is still positive ( $3460 > 0$ ), so we will continue with division.

Step 3 :
Divide $4902$ by $3460$ and get the remainder

4902 : 3460 = 1 ( remainder is 1442)

The remainder is still positive ( $1442 > 0$ ), so we will continue with division.

Step 4 :
Divide $3460$ by $1442$ and get the remainder

3460 : 1442 = 2 ( remainder is 576)

The remainder is still positive ( $576 > 0$ ), so we will continue with division.

Step 5 :
Divide $1442$ by $576$ and get the remainder

1442 : 576 = 2 ( remainder is 290)

The remainder is still positive ( $290 > 0$ ), so we will continue with division.

Step 6 :
Divide $576$ by $290$ and get the remainder

576 : 290 = 1 ( remainder is 286)

The remainder is still positive ( $286 > 0$ ), so we will continue with division.

Step 7 :
Divide $290$ by $286$ and get the remainder

290 : 286 = 1 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 8 :
Divide $286$ by $4$ and get the remainder

286 : 4 = 71 ( remainder is 2)

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

Step 9 :
Divide $4$ by $2$ and get the remainder

4 : 2 = 2 ( 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

765844

8362

191461

113

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

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