Question

Find Greatest Common Divisor of 300 and 110, using Euclidean algorithm.

Answer

The GCD of given numbers is 10.

Explanation

Step 1 :
Divide $300$ by $110$ and get the remainder

300 : 110 = 2 ( remainder is 80)

The remainder is positive ( $80 > 0$ ), so we will continue with division.

Step 2 :
Divide $110$ by $80$ and get the remainder

110 : 80 = 1 ( remainder is 30)

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

Step 3 :
Divide $80$ by $30$ and get the remainder

80 : 30 = 2 ( remainder is 20)

The remainder is still positive ( $20 > 0$ ), so we will continue with division.

Step 4 :
Divide $30$ by $20$ and get the remainder

30 : 20 = 1 ( remainder is 10)

The remainder is still positive ( $10 > 0$ ), so we will continue with division.

Step 5 :
Divide $20$ by $10$ and get the remainder

20 : 10 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $10$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

300

110

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

This page was created using

GCD Calculator