Question

Find Greatest Common Divisor of 2468 and 1357, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $2468$ by $1357$ and get the remainder

2468 : 1357 = 1 ( remainder is 1111)

The remainder is positive ( $1111 > 0$ ), so we will continue with division.

Step 2 :
Divide $1357$ by $1111$ and get the remainder

1357 : 1111 = 1 ( remainder is 246)

The remainder is still positive ( $246 > 0$ ), so we will continue with division.

Step 3 :
Divide $1111$ by $246$ and get the remainder

1111 : 246 = 4 ( remainder is 127)

The remainder is still positive ( $127 > 0$ ), so we will continue with division.

Step 4 :
Divide $246$ by $127$ and get the remainder

246 : 127 = 1 ( remainder is 119)

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

Step 5 :
Divide $127$ by $119$ and get the remainder

127 : 119 = 1 ( remainder is 8)

The remainder is still positive ( $8 > 0$ ), so we will continue with division.

Step 6 :
Divide $119$ by $8$ and get the remainder

119 : 8 = 14 ( remainder is 7)

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

Step 7 :
Divide $8$ by $7$ and get the remainder

8 : 7 = 1 ( remainder is 1)

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

Step 8 :
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

2468

1357

617

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

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