Question

Find Greatest Common Divisor of 1739 and 9923, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $9923$ by $1739$ and get the remainder

9923 : 1739 = 5 ( remainder is 1228)

The remainder is positive ( $1228 > 0$ ), so we will continue with division.

Step 2 :
Divide $1739$ by $1228$ and get the remainder

1739 : 1228 = 1 ( remainder is 511)

The remainder is still positive ( $511 > 0$ ), so we will continue with division.

Step 3 :
Divide $1228$ by $511$ and get the remainder

1228 : 511 = 2 ( remainder is 206)

The remainder is still positive ( $206 > 0$ ), so we will continue with division.

Step 4 :
Divide $511$ by $206$ and get the remainder

511 : 206 = 2 ( remainder is 99)

The remainder is still positive ( $99 > 0$ ), so we will continue with division.

Step 5 :
Divide $206$ by $99$ and get the remainder

206 : 99 = 2 ( remainder is 8)

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

Step 6 :
Divide $99$ by $8$ and get the remainder

99 : 8 = 12 ( remainder is 3)

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

Step 7 :
Divide $8$ by $3$ and get the remainder

8 : 3 = 2 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 8 :
Divide $3$ by $2$ and get the remainder

3 : 2 = 1 ( remainder is 1)

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

Step 9 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( 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

1739

9923

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

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