Question

Find Greatest Common Divisor of 35742 and 13566, using Euclidean algorithm.

Answer

The GCD of given numbers is 42.

Explanation

Step 1 :
Divide $35742$ by $13566$ and get the remainder

35742 : 13566 = 2 ( remainder is 8610)

The remainder is positive ( $8610 > 0$ ), so we will continue with division.

Step 2 :
Divide $13566$ by $8610$ and get the remainder

13566 : 8610 = 1 ( remainder is 4956)

The remainder is still positive ( $4956 > 0$ ), so we will continue with division.

Step 3 :
Divide $8610$ by $4956$ and get the remainder

8610 : 4956 = 1 ( remainder is 3654)

The remainder is still positive ( $3654 > 0$ ), so we will continue with division.

Step 4 :
Divide $4956$ by $3654$ and get the remainder

4956 : 3654 = 1 ( remainder is 1302)

The remainder is still positive ( $1302 > 0$ ), so we will continue with division.

Step 5 :
Divide $3654$ by $1302$ and get the remainder

3654 : 1302 = 2 ( remainder is 1050)

The remainder is still positive ( $1050 > 0$ ), so we will continue with division.

Step 6 :
Divide $1302$ by $1050$ and get the remainder

1302 : 1050 = 1 ( remainder is 252)

The remainder is still positive ( $252 > 0$ ), so we will continue with division.

Step 7 :
Divide $1050$ by $252$ and get the remainder

1050 : 252 = 4 ( remainder is 42)

The remainder is still positive ( $42 > 0$ ), so we will continue with division.

Step 8 :
Divide $252$ by $42$ and get the remainder

252 : 42 = 6 ( remainder is 0)

The remainder is zero => GCD is the last divisor $42$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

35742

13566

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

This page was created using

GCD Calculator