Question

Find Greatest Common Divisor of 1028 and 576, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $1028$ by $576$ and get the remainder

1028 : 576 = 1 ( remainder is 452)

The remainder is positive ( $452 > 0$ ), so we will continue with division.

Step 2 :
Divide $576$ by $452$ and get the remainder

576 : 452 = 1 ( remainder is 124)

The remainder is still positive ( $124 > 0$ ), so we will continue with division.

Step 3 :
Divide $452$ by $124$ and get the remainder

452 : 124 = 3 ( remainder is 80)

The remainder is still positive ( $80 > 0$ ), so we will continue with division.

Step 4 :
Divide $124$ by $80$ and get the remainder

124 : 80 = 1 ( remainder is 44)

The remainder is still positive ( $44 > 0$ ), so we will continue with division.

Step 5 :
Divide $80$ by $44$ and get the remainder

80 : 44 = 1 ( remainder is 36)

The remainder is still positive ( $36 > 0$ ), so we will continue with division.

Step 6 :
Divide $44$ by $36$ and get the remainder

44 : 36 = 1 ( remainder is 8)

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

Step 7 :
Divide $36$ by $8$ and get the remainder

36 : 8 = 4 ( remainder is 4)

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

Step 8 :
Divide $8$ by $4$ and get the remainder

8 : 4 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $4$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1028

576

257

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

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