Question

Find Greatest Common Divisor of 34 and 55, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $55$ by $34$ and get the remainder

55 : 34 = 1 ( remainder is 21)

The remainder is positive ( $21 > 0$ ), so we will continue with division.

Step 2 :
Divide $34$ by $21$ and get the remainder

34 : 21 = 1 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 3 :
Divide $21$ by $13$ and get the remainder

21 : 13 = 1 ( remainder is 8)

The remainder is still positive ( $8 > 0$ ), so we will continue with division.

Step 4 :
Divide $13$ by $8$ and get the remainder

13 : 8 = 1 ( remainder is 5)

The remainder is still positive ( $5 > 0$ ), so we will continue with division.

Step 5 :
Divide $8$ by $5$ and get the remainder

8 : 5 = 1 ( remainder is 3)

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

Step 6 :
Divide $5$ by $3$ and get the remainder

5 : 3 = 1 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 7 :
Divide $3$ by $2$ and get the remainder

3 : 2 = 1 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 8 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

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

This page was created using

GCD Calculator