Question

Find Greatest Common Divisor of 1100 and 57330, using Euclidean algorithm.

Answer

The GCD of given numbers is 10.

Explanation

Step 1 :
Divide $57330$ by $1100$ and get the remainder

57330 : 1100 = 52 ( remainder is 130)

The remainder is positive ( $130 > 0$ ), so we will continue with division.

Step 2 :
Divide $1100$ by $130$ and get the remainder

1100 : 130 = 8 ( remainder is 60)

The remainder is still positive ( $60 > 0$ ), so we will continue with division.

Step 3 :
Divide $130$ by $60$ and get the remainder

130 : 60 = 2 ( remainder is 10)

The remainder is still positive ( $10 > 0$ ), so we will continue with division.

Step 4 :
Divide $60$ by $10$ and get the remainder

60 : 10 = 6 ( remainder is 0)

The remainder is zero => GCD is the last divisor $10$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1100

57330

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

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