Question

Find Greatest Common Divisor of 987 and 343, using Euclidean algorithm.

Answer

The GCD of given numbers is 7.

Explanation

Step 1 :
Divide $987$ by $343$ and get the remainder

987 : 343 = 2 ( remainder is 301)

The remainder is positive ( $301 > 0$ ), so we will continue with division.

Step 2 :
Divide $343$ by $301$ and get the remainder

343 : 301 = 1 ( remainder is 42)

The remainder is still positive ( $42 > 0$ ), so we will continue with division.

Step 3 :
Divide $301$ by $42$ and get the remainder

301 : 42 = 7 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 4 :
Divide $42$ by $7$ and get the remainder

42 : 7 = 6 ( remainder is 0)

The remainder is zero => GCD is the last divisor $7$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

987

343

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

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