Question

Find Greatest Common Divisor of 2517 and 2370, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $2517$ by $2370$ and get the remainder

2517 : 2370 = 1 ( remainder is 147)

The remainder is positive ( $147 > 0$ ), so we will continue with division.

Step 2 :
Divide $2370$ by $147$ and get the remainder

2370 : 147 = 16 ( remainder is 18)

The remainder is still positive ( $18 > 0$ ), so we will continue with division.

Step 3 :
Divide $147$ by $18$ and get the remainder

147 : 18 = 8 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 4 :
Divide $18$ by $3$ and get the remainder

18 : 3 = 6 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

2517

2370

839

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

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