Question

Find Greatest Common Divisor of 12728 and 20000, using Euclidean algorithm.

Answer

The GCD of given numbers is 8.

Explanation

Step 1 :
Divide $20000$ by $12728$ and get the remainder

20000 : 12728 = 1 ( remainder is 7272)

The remainder is positive ( $7272 > 0$ ), so we will continue with division.

Step 2 :
Divide $12728$ by $7272$ and get the remainder

12728 : 7272 = 1 ( remainder is 5456)

The remainder is still positive ( $5456 > 0$ ), so we will continue with division.

Step 3 :
Divide $7272$ by $5456$ and get the remainder

7272 : 5456 = 1 ( remainder is 1816)

The remainder is still positive ( $1816 > 0$ ), so we will continue with division.

Step 4 :
Divide $5456$ by $1816$ and get the remainder

5456 : 1816 = 3 ( remainder is 8)

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

Step 5 :
Divide $1816$ by $8$ and get the remainder

1816 : 8 = 227 ( remainder is 0)

The remainder is zero => GCD is the last divisor $8$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

12728

20000

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

This page was created using

GCD Calculator