Question

Find Greatest Common Divisor of 6536 and 9503, using Euclidean algorithm.

Answer

The GCD of given numbers is 43.

Explanation

Step 1 :
Divide $9503$ by $6536$ and get the remainder

9503 : 6536 = 1 ( remainder is 2967)

The remainder is positive ( $2967 > 0$ ), so we will continue with division.

Step 2 :
Divide $6536$ by $2967$ and get the remainder

6536 : 2967 = 2 ( remainder is 602)

The remainder is still positive ( $602 > 0$ ), so we will continue with division.

Step 3 :
Divide $2967$ by $602$ and get the remainder

2967 : 602 = 4 ( remainder is 559)

The remainder is still positive ( $559 > 0$ ), so we will continue with division.

Step 4 :
Divide $602$ by $559$ and get the remainder

602 : 559 = 1 ( remainder is 43)

The remainder is still positive ( $43 > 0$ ), so we will continue with division.

Step 5 :
Divide $559$ by $43$ and get the remainder

559 : 43 = 13 ( remainder is 0)

The remainder is zero => GCD is the last divisor $43$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

6536

9503

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

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