Question

Find Greatest Common Divisor of 12075 and 4655, using Euclidean algorithm.

Answer

The GCD of given numbers is 35.

Explanation

Step 1 :
Divide $12075$ by $4655$ and get the remainder

12075 : 4655 = 2 ( remainder is 2765)

The remainder is positive ( $2765 > 0$ ), so we will continue with division.

Step 2 :
Divide $4655$ by $2765$ and get the remainder

4655 : 2765 = 1 ( remainder is 1890)

The remainder is still positive ( $1890 > 0$ ), so we will continue with division.

Step 3 :
Divide $2765$ by $1890$ and get the remainder

2765 : 1890 = 1 ( remainder is 875)

The remainder is still positive ( $875 > 0$ ), so we will continue with division.

Step 4 :
Divide $1890$ by $875$ and get the remainder

1890 : 875 = 2 ( remainder is 140)

The remainder is still positive ( $140 > 0$ ), so we will continue with division.

Step 5 :
Divide $875$ by $140$ and get the remainder

875 : 140 = 6 ( remainder is 35)

The remainder is still positive ( $35 > 0$ ), so we will continue with division.

Step 6 :
Divide $140$ by $35$ and get the remainder

140 : 35 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $35$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

12075

4655

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

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