Question

Find Greatest Common Divisor of 4284 and 8219, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $8219$ by $4284$ and get the remainder

8219 : 4284 = 1 ( remainder is 3935)

The remainder is positive ( $3935 > 0$ ), so we will continue with division.

Step 2 :
Divide $4284$ by $3935$ and get the remainder

4284 : 3935 = 1 ( remainder is 349)

The remainder is still positive ( $349 > 0$ ), so we will continue with division.

Step 3 :
Divide $3935$ by $349$ and get the remainder

3935 : 349 = 11 ( remainder is 96)

The remainder is still positive ( $96 > 0$ ), so we will continue with division.

Step 4 :
Divide $349$ by $96$ and get the remainder

349 : 96 = 3 ( remainder is 61)

The remainder is still positive ( $61 > 0$ ), so we will continue with division.

Step 5 :
Divide $96$ by $61$ and get the remainder

96 : 61 = 1 ( remainder is 35)

The remainder is still positive ( $35 > 0$ ), so we will continue with division.

Step 6 :
Divide $61$ by $35$ and get the remainder

61 : 35 = 1 ( remainder is 26)

The remainder is still positive ( $26 > 0$ ), so we will continue with division.

Step 7 :
Divide $35$ by $26$ and get the remainder

35 : 26 = 1 ( remainder is 9)

The remainder is still positive ( $9 > 0$ ), so we will continue with division.

Step 8 :
Divide $26$ by $9$ and get the remainder

26 : 9 = 2 ( remainder is 8)

The remainder is still positive ( $8 > 0$ ), so we will continue with division.

Step 9 :
Divide $9$ by $8$ and get the remainder

9 : 8 = 1 ( remainder is 1)

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

Step 10 :
Divide $8$ by $1$ and get the remainder

8 : 1 = 8 ( 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

4284

8219

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

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