Question

Find Greatest Common Divisor of 76587 and 836, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $76587$ by $836$ and get the remainder

76587 : 836 = 91 ( remainder is 511)

The remainder is positive ( $511 > 0$ ), so we will continue with division.

Step 2 :
Divide $836$ by $511$ and get the remainder

836 : 511 = 1 ( remainder is 325)

The remainder is still positive ( $325 > 0$ ), so we will continue with division.

Step 3 :
Divide $511$ by $325$ and get the remainder

511 : 325 = 1 ( remainder is 186)

The remainder is still positive ( $186 > 0$ ), so we will continue with division.

Step 4 :
Divide $325$ by $186$ and get the remainder

325 : 186 = 1 ( remainder is 139)

The remainder is still positive ( $139 > 0$ ), so we will continue with division.

Step 5 :
Divide $186$ by $139$ and get the remainder

186 : 139 = 1 ( remainder is 47)

The remainder is still positive ( $47 > 0$ ), so we will continue with division.

Step 6 :
Divide $139$ by $47$ and get the remainder

139 : 47 = 2 ( remainder is 45)

The remainder is still positive ( $45 > 0$ ), so we will continue with division.

Step 7 :
Divide $47$ by $45$ and get the remainder

47 : 45 = 1 ( remainder is 2)

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

Step 8 :
Divide $45$ by $2$ and get the remainder

45 : 2 = 22 ( 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

76587

836

521

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

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