Question

Find Greatest Common Divisor of 54321 and 9876, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $54321$ by $9876$ and get the remainder

54321 : 9876 = 5 ( remainder is 4941)

The remainder is positive ( $4941 > 0$ ), so we will continue with division.

Step 2 :
Divide $9876$ by $4941$ and get the remainder

9876 : 4941 = 1 ( remainder is 4935)

The remainder is still positive ( $4935 > 0$ ), so we will continue with division.

Step 3 :
Divide $4941$ by $4935$ and get the remainder

4941 : 4935 = 1 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 4 :
Divide $4935$ by $6$ and get the remainder

4935 : 6 = 822 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 5 :
Divide $6$ by $3$ and get the remainder

6 : 3 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

54321

9876

953

823

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

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