Question

Find Greatest Common Divisor of 1009 and 958, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $1009$ by $958$ and get the remainder

1009 : 958 = 1 ( remainder is 51)

The remainder is positive ( $51 > 0$ ), so we will continue with division.

Step 2 :
Divide $958$ by $51$ and get the remainder

958 : 51 = 18 ( remainder is 40)

The remainder is still positive ( $40 > 0$ ), so we will continue with division.

Step 3 :
Divide $51$ by $40$ and get the remainder

51 : 40 = 1 ( remainder is 11)

The remainder is still positive ( $11 > 0$ ), so we will continue with division.

Step 4 :
Divide $40$ by $11$ and get the remainder

40 : 11 = 3 ( remainder is 7)

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

Step 5 :
Divide $11$ by $7$ and get the remainder

11 : 7 = 1 ( remainder is 4)

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

Step 6 :
Divide $7$ by $4$ and get the remainder

7 : 4 = 1 ( 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

1009

958

1009

479

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

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