Question

Find Greatest Common Divisor of 28260 and 5148, using Euclidean algorithm.

Answer

The GCD of given numbers is 36.

Explanation

Step 1 :
Divide $28260$ by $5148$ and get the remainder

28260 : 5148 = 5 ( remainder is 2520)

The remainder is positive ( $2520 > 0$ ), so we will continue with division.

Step 2 :
Divide $5148$ by $2520$ and get the remainder

5148 : 2520 = 2 ( remainder is 108)

The remainder is still positive ( $108 > 0$ ), so we will continue with division.

Step 3 :
Divide $2520$ by $108$ and get the remainder

2520 : 108 = 23 ( remainder is 36)

The remainder is still positive ( $36 > 0$ ), so we will continue with division.

Step 4 :
Divide $108$ by $36$ and get the remainder

108 : 36 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $36$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

28260

5148

157

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

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