Question

Find Greatest Common Divisor of 616 and 426, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $616$ by $426$ and get the remainder

616 : 426 = 1 ( remainder is 190)

The remainder is positive ( $190 > 0$ ), so we will continue with division.

Step 2 :
Divide $426$ by $190$ and get the remainder

426 : 190 = 2 ( remainder is 46)

The remainder is still positive ( $46 > 0$ ), so we will continue with division.

Step 3 :
Divide $190$ by $46$ and get the remainder

190 : 46 = 4 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 4 :
Divide $46$ by $6$ and get the remainder

46 : 6 = 7 ( remainder is 4)

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

Step 5 :
Divide $6$ by $4$ and get the remainder

6 : 4 = 1 ( remainder is 2)

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

Step 6 :
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

616

426

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

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