Question

Find Greatest Common Divisor of 10672 and 4147, using Euclidean algorithm.

Answer

The GCD of given numbers is 29.

Explanation

Step 1 :
Divide $10672$ by $4147$ and get the remainder

10672 : 4147 = 2 ( remainder is 2378)

The remainder is positive ( $2378 > 0$ ), so we will continue with division.

Step 2 :
Divide $4147$ by $2378$ and get the remainder

4147 : 2378 = 1 ( remainder is 1769)

The remainder is still positive ( $1769 > 0$ ), so we will continue with division.

Step 3 :
Divide $2378$ by $1769$ and get the remainder

2378 : 1769 = 1 ( remainder is 609)

The remainder is still positive ( $609 > 0$ ), so we will continue with division.

Step 4 :
Divide $1769$ by $609$ and get the remainder

1769 : 609 = 2 ( remainder is 551)

The remainder is still positive ( $551 > 0$ ), so we will continue with division.

Step 5 :
Divide $609$ by $551$ and get the remainder

609 : 551 = 1 ( remainder is 58)

The remainder is still positive ( $58 > 0$ ), so we will continue with division.

Step 6 :
Divide $551$ by $58$ and get the remainder

551 : 58 = 9 ( remainder is 29)

The remainder is still positive ( $29 > 0$ ), so we will continue with division.

Step 7 :
Divide $58$ by $29$ and get the remainder

58 : 29 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $29$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

10672

4147

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

This page was created using

GCD Calculator