Question

Find Greatest Common Divisor of 97 and 1045, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $1045$ by $97$ and get the remainder

1045 : 97 = 10 ( remainder is 75)

The remainder is positive ( $75 > 0$ ), so we will continue with division.

Step 2 :
Divide $97$ by $75$ and get the remainder

97 : 75 = 1 ( remainder is 22)

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

Step 3 :
Divide $75$ by $22$ and get the remainder

75 : 22 = 3 ( remainder is 9)

The remainder is still positive ( $9 > 0$ ), so we will continue with division.

Step 4 :
Divide $22$ by $9$ and get the remainder

22 : 9 = 2 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 5 :
Divide $9$ by $4$ and get the remainder

9 : 4 = 2 ( remainder is 1)

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

Step 6 :
Divide $4$ by $1$ and get the remainder

4 : 1 = 4 ( 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

1045

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

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