Question

Find Greatest Common Divisor of 2516 and 1125, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $2516$ by $1125$ and get the remainder

2516 : 1125 = 2 ( remainder is 266)

The remainder is positive ( $266 > 0$ ), so we will continue with division.

Step 2 :
Divide $1125$ by $266$ and get the remainder

1125 : 266 = 4 ( remainder is 61)

The remainder is still positive ( $61 > 0$ ), so we will continue with division.

Step 3 :
Divide $266$ by $61$ and get the remainder

266 : 61 = 4 ( remainder is 22)

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

Step 4 :
Divide $61$ by $22$ and get the remainder

61 : 22 = 2 ( remainder is 17)

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

Step 5 :
Divide $22$ by $17$ and get the remainder

22 : 17 = 1 ( remainder is 5)

The remainder is still positive ( $5 > 0$ ), so we will continue with division.

Step 6 :
Divide $17$ by $5$ and get the remainder

17 : 5 = 3 ( remainder is 2)

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

Step 7 :
Divide $5$ by $2$ and get the remainder

5 : 2 = 2 ( remainder is 1)

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

Step 8 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( 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

2516

1125

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

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