Question

Find Greatest Common Divisor of 1056 and 228, using Euclidean algorithm.

Answer

The GCD of given numbers is 12.

Explanation

Step 1 :
Divide $1056$ by $228$ and get the remainder

1056 : 228 = 4 ( remainder is 144)

The remainder is positive ( $144 > 0$ ), so we will continue with division.

Step 2 :
Divide $228$ by $144$ and get the remainder

228 : 144 = 1 ( remainder is 84)

The remainder is still positive ( $84 > 0$ ), so we will continue with division.

Step 3 :
Divide $144$ by $84$ and get the remainder

144 : 84 = 1 ( remainder is 60)

The remainder is still positive ( $60 > 0$ ), so we will continue with division.

Step 4 :
Divide $84$ by $60$ and get the remainder

84 : 60 = 1 ( remainder is 24)

The remainder is still positive ( $24 > 0$ ), so we will continue with division.

Step 5 :
Divide $60$ by $24$ and get the remainder

60 : 24 = 2 ( remainder is 12)

The remainder is still positive ( $12 > 0$ ), so we will continue with division.

Step 6 :
Divide $24$ by $12$ and get the remainder

24 : 12 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $12$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1056

228

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

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