Question

Find Greatest Common Divisor of 289 and 377, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $377$ by $289$ and get the remainder

377 : 289 = 1 ( remainder is 88)

The remainder is positive ( $88 > 0$ ), so we will continue with division.

Step 2 :
Divide $289$ by $88$ and get the remainder

289 : 88 = 3 ( remainder is 25)

The remainder is still positive ( $25 > 0$ ), so we will continue with division.

Step 3 :
Divide $88$ by $25$ and get the remainder

88 : 25 = 3 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 4 :
Divide $25$ by $13$ and get the remainder

25 : 13 = 1 ( remainder is 12)

The remainder is still positive ( $12 > 0$ ), so we will continue with division.

Step 5 :
Divide $13$ by $12$ and get the remainder

13 : 12 = 1 ( remainder is 1)

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

Step 6 :
Divide $12$ by $1$ and get the remainder

12 : 1 = 12 ( 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

289

377

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

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