Question

Find Greatest Common Divisor of 6638 and 22783, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $22783$ by $6638$ and get the remainder

22783 : 6638 = 3 ( remainder is 2869)

The remainder is positive ( $2869 > 0$ ), so we will continue with division.

Step 2 :
Divide $6638$ by $2869$ and get the remainder

6638 : 2869 = 2 ( remainder is 900)

The remainder is still positive ( $900 > 0$ ), so we will continue with division.

Step 3 :
Divide $2869$ by $900$ and get the remainder

2869 : 900 = 3 ( remainder is 169)

The remainder is still positive ( $169 > 0$ ), so we will continue with division.

Step 4 :
Divide $900$ by $169$ and get the remainder

900 : 169 = 5 ( remainder is 55)

The remainder is still positive ( $55 > 0$ ), so we will continue with division.

Step 5 :
Divide $169$ by $55$ and get the remainder

169 : 55 = 3 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 6 :
Divide $55$ by $4$ and get the remainder

55 : 4 = 13 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 7 :
Divide $4$ by $3$ and get the remainder

4 : 3 = 1 ( remainder is 1)

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

Step 8 :
Divide $3$ by $1$ and get the remainder

3 : 1 = 3 ( 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

6638

22783

3319

22783

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

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