Question

Find Greatest Common Divisor of 54796 and 605, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $54796$ by $605$ and get the remainder

54796 : 605 = 90 ( remainder is 346)

The remainder is positive ( $346 > 0$ ), so we will continue with division.

Step 2 :
Divide $605$ by $346$ and get the remainder

605 : 346 = 1 ( remainder is 259)

The remainder is still positive ( $259 > 0$ ), so we will continue with division.

Step 3 :
Divide $346$ by $259$ and get the remainder

346 : 259 = 1 ( remainder is 87)

The remainder is still positive ( $87 > 0$ ), so we will continue with division.

Step 4 :
Divide $259$ by $87$ and get the remainder

259 : 87 = 2 ( remainder is 85)

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

Step 5 :
Divide $87$ by $85$ and get the remainder

87 : 85 = 1 ( remainder is 2)

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

Step 6 :
Divide $85$ by $2$ and get the remainder

85 : 2 = 42 ( remainder is 1)

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

Step 7 :
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

54796

605

103

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

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