Question

Find Greatest Common Divisor of 547 and 189, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $547$ by $189$ and get the remainder

547 : 189 = 2 ( remainder is 169)

The remainder is positive ( $169 > 0$ ), so we will continue with division.

Step 2 :
Divide $189$ by $169$ and get the remainder

189 : 169 = 1 ( remainder is 20)

The remainder is still positive ( $20 > 0$ ), so we will continue with division.

Step 3 :
Divide $169$ by $20$ and get the remainder

169 : 20 = 8 ( remainder is 9)

The remainder is still positive ( $9 > 0$ ), so we will continue with division.

Step 4 :
Divide $20$ by $9$ and get the remainder

20 : 9 = 2 ( remainder is 2)

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

Step 5 :
Divide $9$ by $2$ and get the remainder

9 : 2 = 4 ( remainder is 1)

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

Step 6 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( 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

547

189

547

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

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