Question

Find Greatest Common Divisor of 2024 and 1054, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $2024$ by $1054$ and get the remainder

2024 : 1054 = 1 ( remainder is 970)

The remainder is positive ( $970 > 0$ ), so we will continue with division.

Step 2 :
Divide $1054$ by $970$ and get the remainder

1054 : 970 = 1 ( remainder is 84)

The remainder is still positive ( $84 > 0$ ), so we will continue with division.

Step 3 :
Divide $970$ by $84$ and get the remainder

970 : 84 = 11 ( remainder is 46)

The remainder is still positive ( $46 > 0$ ), so we will continue with division.

Step 4 :
Divide $84$ by $46$ and get the remainder

84 : 46 = 1 ( remainder is 38)

The remainder is still positive ( $38 > 0$ ), so we will continue with division.

Step 5 :
Divide $46$ by $38$ and get the remainder

46 : 38 = 1 ( remainder is 8)

The remainder is still positive ( $8 > 0$ ), so we will continue with division.

Step 6 :
Divide $38$ by $8$ and get the remainder

38 : 8 = 4 ( remainder is 6)

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

Step 7 :
Divide $8$ by $6$ and get the remainder

8 : 6 = 1 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 8 :
Divide $6$ by $2$ and get the remainder

6 : 2 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $2$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

2024

1054

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

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