Question

Find Greatest Common Divisor of 231 and 775, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $775$ by $231$ and get the remainder

775 : 231 = 3 ( remainder is 82)

The remainder is positive ( $82 > 0$ ), so we will continue with division.

Step 2 :
Divide $231$ by $82$ and get the remainder

231 : 82 = 2 ( remainder is 67)

The remainder is still positive ( $67 > 0$ ), so we will continue with division.

Step 3 :
Divide $82$ by $67$ and get the remainder

82 : 67 = 1 ( remainder is 15)

The remainder is still positive ( $15 > 0$ ), so we will continue with division.

Step 4 :
Divide $67$ by $15$ and get the remainder

67 : 15 = 4 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 5 :
Divide $15$ by $7$ and get the remainder

15 : 7 = 2 ( remainder is 1)

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

Step 6 :
Divide $7$ by $1$ and get the remainder

7 : 1 = 7 ( 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

231

775

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

This page was created using

GCD Calculator