Question

Find Greatest Common Divisor of 2437 and 875, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $2437$ by $875$ and get the remainder

2437 : 875 = 2 ( remainder is 687)

The remainder is positive ( $687 > 0$ ), so we will continue with division.

Step 2 :
Divide $875$ by $687$ and get the remainder

875 : 687 = 1 ( remainder is 188)

The remainder is still positive ( $188 > 0$ ), so we will continue with division.

Step 3 :
Divide $687$ by $188$ and get the remainder

687 : 188 = 3 ( remainder is 123)

The remainder is still positive ( $123 > 0$ ), so we will continue with division.

Step 4 :
Divide $188$ by $123$ and get the remainder

188 : 123 = 1 ( remainder is 65)

The remainder is still positive ( $65 > 0$ ), so we will continue with division.

Step 5 :
Divide $123$ by $65$ and get the remainder

123 : 65 = 1 ( remainder is 58)

The remainder is still positive ( $58 > 0$ ), so we will continue with division.

Step 6 :
Divide $65$ by $58$ and get the remainder

65 : 58 = 1 ( remainder is 7)

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

Step 7 :
Divide $58$ by $7$ and get the remainder

58 : 7 = 8 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 8 :
Divide $7$ by $2$ and get the remainder

7 : 2 = 3 ( remainder is 1)

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

Step 9 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( 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

2437

875

2437

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

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