Question

Find Greatest Common Divisor of 1610 and 667, using Euclidean algorithm.

Answer

The GCD of given numbers is 23.

Explanation

Step 1 :
Divide $1610$ by $667$ and get the remainder

1610 : 667 = 2 ( remainder is 276)

The remainder is positive ( $276 > 0$ ), so we will continue with division.

Step 2 :
Divide $667$ by $276$ and get the remainder

667 : 276 = 2 ( remainder is 115)

The remainder is still positive ( $115 > 0$ ), so we will continue with division.

Step 3 :
Divide $276$ by $115$ and get the remainder

276 : 115 = 2 ( remainder is 46)

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

Step 4 :
Divide $115$ by $46$ and get the remainder

115 : 46 = 2 ( remainder is 23)

The remainder is still positive ( $23 > 0$ ), so we will continue with division.

Step 5 :
Divide $46$ by $23$ and get the remainder

46 : 23 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $23$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1610

667

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

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