Question

Find Greatest Common Divisor of 3289 and 2415, using Euclidean algorithm.

Answer

The GCD of given numbers is 23.

Explanation

Step 1 :
Divide $3289$ by $2415$ and get the remainder

3289 : 2415 = 1 ( remainder is 874)

The remainder is positive ( $874 > 0$ ), so we will continue with division.

Step 2 :
Divide $2415$ by $874$ and get the remainder

2415 : 874 = 2 ( remainder is 667)

The remainder is still positive ( $667 > 0$ ), so we will continue with division.

Step 3 :
Divide $874$ by $667$ and get the remainder

874 : 667 = 1 ( remainder is 207)

The remainder is still positive ( $207 > 0$ ), so we will continue with division.

Step 4 :
Divide $667$ by $207$ and get the remainder

667 : 207 = 3 ( remainder is 46)

The remainder is still positive ( $46 > 0$ ), so we will continue with division.

Step 5 :
Divide $207$ by $46$ and get the remainder

207 : 46 = 4 ( remainder is 23)

The remainder is still positive ( $23 > 0$ ), so we will continue with division.

Step 6 :
Divide $46$ by $23$ and get the remainder

46 : 23 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $23$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

3289

2415

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

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