Question

Find Greatest Common Divisor of 2024 and 1061, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $2024$ by $1061$ and get the remainder

2024 : 1061 = 1 ( remainder is 963)

The remainder is positive ( $963 > 0$ ), so we will continue with division.

Step 2 :
Divide $1061$ by $963$ and get the remainder

1061 : 963 = 1 ( remainder is 98)

The remainder is still positive ( $98 > 0$ ), so we will continue with division.

Step 3 :
Divide $963$ by $98$ and get the remainder

963 : 98 = 9 ( remainder is 81)

The remainder is still positive ( $81 > 0$ ), so we will continue with division.

Step 4 :
Divide $98$ by $81$ and get the remainder

98 : 81 = 1 ( remainder is 17)

The remainder is still positive ( $17 > 0$ ), so we will continue with division.

Step 5 :
Divide $81$ by $17$ and get the remainder

81 : 17 = 4 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 6 :
Divide $17$ by $13$ and get the remainder

17 : 13 = 1 ( remainder is 4)

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

Step 7 :
Divide $13$ by $4$ and get the remainder

13 : 4 = 3 ( remainder is 1)

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

Step 8 :
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

2024

1061

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

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