Question

Find Greatest Common Divisor of 507885 and 60808, using Euclidean algorithm.

Answer

The GCD of given numbers is 691.

Explanation

Step 1 :
Divide $507885$ by $60808$ and get the remainder

507885 : 60808 = 8 ( remainder is 21421)

The remainder is positive ( $21421 > 0$ ), so we will continue with division.

Step 2 :
Divide $60808$ by $21421$ and get the remainder

60808 : 21421 = 2 ( remainder is 17966)

The remainder is still positive ( $17966 > 0$ ), so we will continue with division.

Step 3 :
Divide $21421$ by $17966$ and get the remainder

21421 : 17966 = 1 ( remainder is 3455)

The remainder is still positive ( $3455 > 0$ ), so we will continue with division.

Step 4 :
Divide $17966$ by $3455$ and get the remainder

17966 : 3455 = 5 ( remainder is 691)

The remainder is still positive ( $691 > 0$ ), so we will continue with division.

Step 5 :
Divide $3455$ by $691$ and get the remainder

3455 : 691 = 5 ( remainder is 0)

The remainder is zero => GCD is the last divisor $691$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

507885

60808

691

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

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