Question

Find Greatest Common Divisor of 2447 and 3997, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $3997$ by $2447$ and get the remainder

3997 : 2447 = 1 ( remainder is 1550)

The remainder is positive ( $1550 > 0$ ), so we will continue with division.

Step 2 :
Divide $2447$ by $1550$ and get the remainder

2447 : 1550 = 1 ( remainder is 897)

The remainder is still positive ( $897 > 0$ ), so we will continue with division.

Step 3 :
Divide $1550$ by $897$ and get the remainder

1550 : 897 = 1 ( remainder is 653)

The remainder is still positive ( $653 > 0$ ), so we will continue with division.

Step 4 :
Divide $897$ by $653$ and get the remainder

897 : 653 = 1 ( remainder is 244)

The remainder is still positive ( $244 > 0$ ), so we will continue with division.

Step 5 :
Divide $653$ by $244$ and get the remainder

653 : 244 = 2 ( remainder is 165)

The remainder is still positive ( $165 > 0$ ), so we will continue with division.

Step 6 :
Divide $244$ by $165$ and get the remainder

244 : 165 = 1 ( remainder is 79)

The remainder is still positive ( $79 > 0$ ), so we will continue with division.

Step 7 :
Divide $165$ by $79$ and get the remainder

165 : 79 = 2 ( remainder is 7)

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

Step 8 :
Divide $79$ by $7$ and get the remainder

79 : 7 = 11 ( remainder is 2)

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

Step 9 :
Divide $7$ by $2$ and get the remainder

7 : 2 = 3 ( remainder is 1)

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

Step 10 :
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

2447

3997

2447

571

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

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