Question

Find Greatest Common Divisor of 2579 and 2424, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $2579$ by $2424$ and get the remainder

2579 : 2424 = 1 ( remainder is 155)

The remainder is positive ( $155 > 0$ ), so we will continue with division.

Step 2 :
Divide $2424$ by $155$ and get the remainder

2424 : 155 = 15 ( remainder is 99)

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

Step 3 :
Divide $155$ by $99$ and get the remainder

155 : 99 = 1 ( remainder is 56)

The remainder is still positive ( $56 > 0$ ), so we will continue with division.

Step 4 :
Divide $99$ by $56$ and get the remainder

99 : 56 = 1 ( remainder is 43)

The remainder is still positive ( $43 > 0$ ), so we will continue with division.

Step 5 :
Divide $56$ by $43$ and get the remainder

56 : 43 = 1 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 6 :
Divide $43$ by $13$ and get the remainder

43 : 13 = 3 ( remainder is 4)

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

Step 7 :
Divide $13$ by $4$ and get the remainder

13 : 4 = 3 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 8 :
Divide $4$ by $1$ and get the remainder

4 : 1 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

2579

2424

2579

101

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

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