Question

Find Greatest Common Divisor of 2435 and 342, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $2435$ by $342$ and get the remainder

2435 : 342 = 7 ( remainder is 41)

The remainder is positive ( $41 > 0$ ), so we will continue with division.

Step 2 :
Divide $342$ by $41$ and get the remainder

342 : 41 = 8 ( remainder is 14)

The remainder is still positive ( $14 > 0$ ), so we will continue with division.

Step 3 :
Divide $41$ by $14$ and get the remainder

41 : 14 = 2 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 4 :
Divide $14$ by $13$ and get the remainder

14 : 13 = 1 ( remainder is 1)

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

Step 5 :
Divide $13$ by $1$ and get the remainder

13 : 1 = 13 ( 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

2435

342

487

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

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