Question

Find Greatest Common Divisor of 1024 and 486, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $1024$ by $486$ and get the remainder

1024 : 486 = 2 ( remainder is 52)

The remainder is positive ( $52 > 0$ ), so we will continue with division.

Step 2 :
Divide $486$ by $52$ and get the remainder

486 : 52 = 9 ( remainder is 18)

The remainder is still positive ( $18 > 0$ ), so we will continue with division.

Step 3 :
Divide $52$ by $18$ and get the remainder

52 : 18 = 2 ( remainder is 16)

The remainder is still positive ( $16 > 0$ ), so we will continue with division.

Step 4 :
Divide $18$ by $16$ and get the remainder

18 : 16 = 1 ( remainder is 2)

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

Step 5 :
Divide $16$ by $2$ and get the remainder

16 : 2 = 8 ( remainder is 0)

The remainder is zero => GCD is the last divisor $2$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1024

486

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

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