Question

Find Greatest Common Divisor of 6035 and 578, using Euclidean algorithm.

Answer

The GCD of given numbers is 17.

Explanation

Step 1 :
Divide $6035$ by $578$ and get the remainder

6035 : 578 = 10 ( remainder is 255)

The remainder is positive ( $255 > 0$ ), so we will continue with division.

Step 2 :
Divide $578$ by $255$ and get the remainder

578 : 255 = 2 ( remainder is 68)

The remainder is still positive ( $68 > 0$ ), so we will continue with division.

Step 3 :
Divide $255$ by $68$ and get the remainder

255 : 68 = 3 ( remainder is 51)

The remainder is still positive ( $51 > 0$ ), so we will continue with division.

Step 4 :
Divide $68$ by $51$ and get the remainder

68 : 51 = 1 ( remainder is 17)

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

Step 5 :
Divide $51$ by $17$ and get the remainder

51 : 17 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $17$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

6035

578

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

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