Question

Find Greatest Common Divisor of 7871850 and 21829500, using Euclidean algorithm.

Answer

The GCD of given numbers is 66150.

Explanation

Step 1 :
Divide $21829500$ by $7871850$ and get the remainder

21829500 : 7871850 = 2 ( remainder is 6085800)

The remainder is positive ( $6085800 > 0$ ), so we will continue with division.

Step 2 :
Divide $7871850$ by $6085800$ and get the remainder

7871850 : 6085800 = 1 ( remainder is 1786050)

The remainder is still positive ( $1786050 > 0$ ), so we will continue with division.

Step 3 :
Divide $6085800$ by $1786050$ and get the remainder

6085800 : 1786050 = 3 ( remainder is 727650)

The remainder is still positive ( $727650 > 0$ ), so we will continue with division.

Step 4 :
Divide $1786050$ by $727650$ and get the remainder

1786050 : 727650 = 2 ( remainder is 330750)

The remainder is still positive ( $330750 > 0$ ), so we will continue with division.

Step 5 :
Divide $727650$ by $330750$ and get the remainder

727650 : 330750 = 2 ( remainder is 66150)

The remainder is still positive ( $66150 > 0$ ), so we will continue with division.

Step 6 :
Divide $330750$ by $66150$ and get the remainder

330750 : 66150 = 5 ( remainder is 0)

The remainder is zero => GCD is the last divisor $66150$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

7871850

21829500

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

This page was created using

GCD Calculator