Question

Find Greatest Common Divisor of 1716 and 1260, using Euclidean algorithm.

Answer

The GCD of given numbers is 12.

Explanation

Step 1 :
Divide $1716$ by $1260$ and get the remainder

1716 : 1260 = 1 ( remainder is 456)

The remainder is positive ( $456 > 0$ ), so we will continue with division.

Step 2 :
Divide $1260$ by $456$ and get the remainder

1260 : 456 = 2 ( remainder is 348)

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

Step 3 :
Divide $456$ by $348$ and get the remainder

456 : 348 = 1 ( remainder is 108)

The remainder is still positive ( $108 > 0$ ), so we will continue with division.

Step 4 :
Divide $348$ by $108$ and get the remainder

348 : 108 = 3 ( remainder is 24)

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

Step 5 :
Divide $108$ by $24$ and get the remainder

108 : 24 = 4 ( 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

1716

1260

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

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