Question

Find Greatest Common Divisor of 280 and 117, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $280$ by $117$ and get the remainder

280 : 117 = 2 ( remainder is 46)

The remainder is positive ( $46 > 0$ ), so we will continue with division.

Step 2 :
Divide $117$ by $46$ and get the remainder

117 : 46 = 2 ( remainder is 25)

The remainder is still positive ( $25 > 0$ ), so we will continue with division.

Step 3 :
Divide $46$ by $25$ and get the remainder

46 : 25 = 1 ( remainder is 21)

The remainder is still positive ( $21 > 0$ ), so we will continue with division.

Step 4 :
Divide $25$ by $21$ and get the remainder

25 : 21 = 1 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 5 :
Divide $21$ by $4$ and get the remainder

21 : 4 = 5 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 6 :
Divide $4$ by $1$ and get the remainder

4 : 1 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

280

117

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

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