Question

Find Greatest Common Divisor of 1258 and 527, using Euclidean algorithm.

Answer

The GCD of given numbers is 17.

Explanation

Step 1 :
Divide $1258$ by $527$ and get the remainder

1258 : 527 = 2 ( remainder is 204)

The remainder is positive ( $204 > 0$ ), so we will continue with division.

Step 2 :
Divide $527$ by $204$ and get the remainder

527 : 204 = 2 ( remainder is 119)

The remainder is still positive ( $119 > 0$ ), so we will continue with division.

Step 3 :
Divide $204$ by $119$ and get the remainder

204 : 119 = 1 ( remainder is 85)

The remainder is still positive ( $85 > 0$ ), so we will continue with division.

Step 4 :
Divide $119$ by $85$ and get the remainder

119 : 85 = 1 ( remainder is 34)

The remainder is still positive ( $34 > 0$ ), so we will continue with division.

Step 5 :
Divide $85$ by $34$ and get the remainder

85 : 34 = 2 ( remainder is 17)

The remainder is still positive ( $17 > 0$ ), so we will continue with division.

Step 6 :
Divide $34$ by $17$ and get the remainder

34 : 17 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $17$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1258

527

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

This page was created using

GCD Calculator