Question

Find Greatest Common Divisor of 987 and 3443, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $3443$ by $987$ and get the remainder

3443 : 987 = 3 ( remainder is 482)

The remainder is positive ( $482 > 0$ ), so we will continue with division.

Step 2 :
Divide $987$ by $482$ and get the remainder

987 : 482 = 2 ( remainder is 23)

The remainder is still positive ( $23 > 0$ ), so we will continue with division.

Step 3 :
Divide $482$ by $23$ and get the remainder

482 : 23 = 20 ( remainder is 22)

The remainder is still positive ( $22 > 0$ ), so we will continue with division.

Step 4 :
Divide $23$ by $22$ and get the remainder

23 : 22 = 1 ( remainder is 1)

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

Step 5 :
Divide $22$ by $1$ and get the remainder

22 : 1 = 22 ( 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

987

3443

313

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

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