Question

Find Greatest Common Divisor of 28458 and 5280, using Euclidean algorithm.

Answer

The GCD of given numbers is 6.

Explanation

Step 1 :
Divide $28458$ by $5280$ and get the remainder

28458 : 5280 = 5 ( remainder is 2058)

The remainder is positive ( $2058 > 0$ ), so we will continue with division.

Step 2 :
Divide $5280$ by $2058$ and get the remainder

5280 : 2058 = 2 ( remainder is 1164)

The remainder is still positive ( $1164 > 0$ ), so we will continue with division.

Step 3 :
Divide $2058$ by $1164$ and get the remainder

2058 : 1164 = 1 ( remainder is 894)

The remainder is still positive ( $894 > 0$ ), so we will continue with division.

Step 4 :
Divide $1164$ by $894$ and get the remainder

1164 : 894 = 1 ( remainder is 270)

The remainder is still positive ( $270 > 0$ ), so we will continue with division.

Step 5 :
Divide $894$ by $270$ and get the remainder

894 : 270 = 3 ( remainder is 84)

The remainder is still positive ( $84 > 0$ ), so we will continue with division.

Step 6 :
Divide $270$ by $84$ and get the remainder

270 : 84 = 3 ( remainder is 18)

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

Step 7 :
Divide $84$ by $18$ and get the remainder

84 : 18 = 4 ( remainder is 12)

The remainder is still positive ( $12 > 0$ ), so we will continue with division.

Step 8 :
Divide $18$ by $12$ and get the remainder

18 : 12 = 1 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 9 :
Divide $12$ by $6$ and get the remainder

12 : 6 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $6$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

28458

5280

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

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