Question

Find Greatest Common Divisor of 4884 and 5365, using Euclidean algorithm.

Answer

The GCD of given numbers is 37.

Explanation

Step 1 :
Divide $5365$ by $4884$ and get the remainder

5365 : 4884 = 1 ( remainder is 481)

The remainder is positive ( $481 > 0$ ), so we will continue with division.

Step 2 :
Divide $4884$ by $481$ and get the remainder

4884 : 481 = 10 ( remainder is 74)

The remainder is still positive ( $74 > 0$ ), so we will continue with division.

Step 3 :
Divide $481$ by $74$ and get the remainder

481 : 74 = 6 ( remainder is 37)

The remainder is still positive ( $37 > 0$ ), so we will continue with division.

Step 4 :
Divide $74$ by $37$ and get the remainder

74 : 37 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $37$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

4884

5365

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

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