Question

Find Greatest Common Divisor of 1024 and 2256, using Euclidean algorithm.

Answer

The GCD of given numbers is 16.

Explanation

Step 1 :
Divide $2256$ by $1024$ and get the remainder

2256 : 1024 = 2 ( remainder is 208)

The remainder is positive ( $208 > 0$ ), so we will continue with division.

Step 2 :
Divide $1024$ by $208$ and get the remainder

1024 : 208 = 4 ( remainder is 192)

The remainder is still positive ( $192 > 0$ ), so we will continue with division.

Step 3 :
Divide $208$ by $192$ and get the remainder

208 : 192 = 1 ( remainder is 16)

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

Step 4 :
Divide $192$ by $16$ and get the remainder

192 : 16 = 12 ( remainder is 0)

The remainder is zero => GCD is the last divisor $16$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1024

2256

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

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