Question

Find Greatest Common Divisor of 1472 and 1124, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $1472$ by $1124$ and get the remainder

1472 : 1124 = 1 ( remainder is 348)

The remainder is positive ( $348 > 0$ ), so we will continue with division.

Step 2 :
Divide $1124$ by $348$ and get the remainder

1124 : 348 = 3 ( remainder is 80)

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

Step 3 :
Divide $348$ by $80$ and get the remainder

348 : 80 = 4 ( remainder is 28)

The remainder is still positive ( $28 > 0$ ), so we will continue with division.

Step 4 :
Divide $80$ by $28$ and get the remainder

80 : 28 = 2 ( remainder is 24)

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

Step 5 :
Divide $28$ by $24$ and get the remainder

28 : 24 = 1 ( remainder is 4)

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

Step 6 :
Divide $24$ by $4$ and get the remainder

24 : 4 = 6 ( 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

1472

1124

281

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

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