Question

Find Greatest Common Divisor of 415 and 142, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $415$ by $142$ and get the remainder

415 : 142 = 2 ( remainder is 131)

The remainder is positive ( $131 > 0$ ), so we will continue with division.

Step 2 :
Divide $142$ by $131$ and get the remainder

142 : 131 = 1 ( remainder is 11)

The remainder is still positive ( $11 > 0$ ), so we will continue with division.

Step 3 :
Divide $131$ by $11$ and get the remainder

131 : 11 = 11 ( remainder is 10)

The remainder is still positive ( $10 > 0$ ), so we will continue with division.

Step 4 :
Divide $11$ by $10$ and get the remainder

11 : 10 = 1 ( remainder is 1)

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

Step 5 :
Divide $10$ by $1$ and get the remainder

10 : 1 = 10 ( 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

415

142

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

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