Question

Find Greatest Common Divisor of 1299 and 1599, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $1599$ by $1299$ and get the remainder

1599 : 1299 = 1 ( remainder is 300)

The remainder is positive ( $300 > 0$ ), so we will continue with division.

Step 2 :
Divide $1299$ by $300$ and get the remainder

1299 : 300 = 4 ( remainder is 99)

The remainder is still positive ( $99 > 0$ ), so we will continue with division.

Step 3 :
Divide $300$ by $99$ and get the remainder

300 : 99 = 3 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 4 :
Divide $99$ by $3$ and get the remainder

99 : 3 = 33 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1299

1599

433

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

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