Question

Find Greatest Common Divisor of 165 and 285, using Euclidean algorithm.

Answer

The GCD of given numbers is 15.

Explanation

Step 1 :
Divide $285$ by $165$ and get the remainder

285 : 165 = 1 ( remainder is 120)

The remainder is positive ( $120 > 0$ ), so we will continue with division.

Step 2 :
Divide $165$ by $120$ and get the remainder

165 : 120 = 1 ( remainder is 45)

The remainder is still positive ( $45 > 0$ ), so we will continue with division.

Step 3 :
Divide $120$ by $45$ and get the remainder

120 : 45 = 2 ( remainder is 30)

The remainder is still positive ( $30 > 0$ ), so we will continue with division.

Step 4 :
Divide $45$ by $30$ and get the remainder

45 : 30 = 1 ( remainder is 15)

The remainder is still positive ( $15 > 0$ ), so we will continue with division.

Step 5 :
Divide $30$ by $15$ and get the remainder

30 : 15 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $15$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

165

285

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

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