Question

Find Greatest Common Divisor of 765844 and 8365, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $765844$ by $8365$ and get the remainder

765844 : 8365 = 91 ( remainder is 4629)

The remainder is positive ( $4629 > 0$ ), so we will continue with division.

Step 2 :
Divide $8365$ by $4629$ and get the remainder

8365 : 4629 = 1 ( remainder is 3736)

The remainder is still positive ( $3736 > 0$ ), so we will continue with division.

Step 3 :
Divide $4629$ by $3736$ and get the remainder

4629 : 3736 = 1 ( remainder is 893)

The remainder is still positive ( $893 > 0$ ), so we will continue with division.

Step 4 :
Divide $3736$ by $893$ and get the remainder

3736 : 893 = 4 ( remainder is 164)

The remainder is still positive ( $164 > 0$ ), so we will continue with division.

Step 5 :
Divide $893$ by $164$ and get the remainder

893 : 164 = 5 ( remainder is 73)

The remainder is still positive ( $73 > 0$ ), so we will continue with division.

Step 6 :
Divide $164$ by $73$ and get the remainder

164 : 73 = 2 ( remainder is 18)

The remainder is still positive ( $18 > 0$ ), so we will continue with division.

Step 7 :
Divide $73$ by $18$ and get the remainder

73 : 18 = 4 ( remainder is 1)

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

Step 8 :
Divide $18$ by $1$ and get the remainder

18 : 1 = 18 ( 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

765844

8365

191461

239

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

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