Question

Find Greatest Common Divisor of 509 and 1177, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $1177$ by $509$ and get the remainder

1177 : 509 = 2 ( remainder is 159)

The remainder is positive ( $159 > 0$ ), so we will continue with division.

Step 2 :
Divide $509$ by $159$ and get the remainder

509 : 159 = 3 ( remainder is 32)

The remainder is still positive ( $32 > 0$ ), so we will continue with division.

Step 3 :
Divide $159$ by $32$ and get the remainder

159 : 32 = 4 ( remainder is 31)

The remainder is still positive ( $31 > 0$ ), so we will continue with division.

Step 4 :
Divide $32$ by $31$ and get the remainder

32 : 31 = 1 ( remainder is 1)

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

Step 5 :
Divide $31$ by $1$ and get the remainder

31 : 1 = 31 ( 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

509

1177

509

107

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

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