Question

Find Greatest Common Divisor of 357 and 221, using Euclidean algorithm.

Answer

The GCD of given numbers is 17.

Explanation

Step 1 :
Divide $357$ by $221$ and get the remainder

357 : 221 = 1 ( remainder is 136)

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

Step 2 :
Divide $221$ by $136$ and get the remainder

221 : 136 = 1 ( remainder is 85)

The remainder is still positive ( $85 > 0$ ), so we will continue with division.

Step 3 :
Divide $136$ by $85$ and get the remainder

136 : 85 = 1 ( remainder is 51)

The remainder is still positive ( $51 > 0$ ), so we will continue with division.

Step 4 :
Divide $85$ by $51$ and get the remainder

85 : 51 = 1 ( remainder is 34)

The remainder is still positive ( $34 > 0$ ), so we will continue with division.

Step 5 :
Divide $51$ by $34$ and get the remainder

51 : 34 = 1 ( remainder is 17)

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

Step 6 :
Divide $34$ by $17$ and get the remainder

34 : 17 = 2 ( 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

357

221

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

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