Question

Find Greatest Common Divisor of 483 and 360, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $483$ by $360$ and get the remainder

483 : 360 = 1 ( remainder is 123)

The remainder is positive ( $123 > 0$ ), so we will continue with division.

Step 2 :
Divide $360$ by $123$ and get the remainder

360 : 123 = 2 ( remainder is 114)

The remainder is still positive ( $114 > 0$ ), so we will continue with division.

Step 3 :
Divide $123$ by $114$ and get the remainder

123 : 114 = 1 ( remainder is 9)

The remainder is still positive ( $9 > 0$ ), so we will continue with division.

Step 4 :
Divide $114$ by $9$ and get the remainder

114 : 9 = 12 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 5 :
Divide $9$ by $6$ and get the remainder

9 : 6 = 1 ( remainder is 3)

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

Step 6 :
Divide $6$ by $3$ and get the remainder

6 : 3 = 2 ( 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

483

360

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

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