Question

Find Greatest Common Divisor of 663 and 5168, using Euclidean algorithm.

Answer

The GCD of given numbers is 17.

Explanation

Step 1 :
Divide $5168$ by $663$ and get the remainder

5168 : 663 = 7 ( remainder is 527)

The remainder is positive ( $527 > 0$ ), so we will continue with division.

Step 2 :
Divide $663$ by $527$ and get the remainder

663 : 527 = 1 ( remainder is 136)

The remainder is still positive ( $136 > 0$ ), so we will continue with division.

Step 3 :
Divide $527$ by $136$ and get the remainder

527 : 136 = 3 ( remainder is 119)

The remainder is still positive ( $119 > 0$ ), so we will continue with division.

Step 4 :
Divide $136$ by $119$ and get the remainder

136 : 119 = 1 ( remainder is 17)

The remainder is still positive ( $17 > 0$ ), so we will continue with division.

Step 5 :
Divide $119$ by $17$ and get the remainder

119 : 17 = 7 ( remainder is 0)

The remainder is zero => GCD is the last divisor $17$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

663

5168

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

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